Identifying an axis of a stimulated reservoir volume for a stimulation treatment of a subterranean region

ABSTRACT

In some aspects, a boundary is computed based on locations of microseismic events associated with a stimulation treatment of a subterranean region. A major axis of a stimulated reservoir volume (SRV) for the stimulation treatment is identified based on the boundary. In some examples, the boundary is an ellipsoid, and the major axis of the ellipsoid is identified.

BACKGROUND

The following description relates to identifying a stimulated reservoirvolume (SRV) for a stimulation treatment of a subterranean region.Microseismic data are often acquired in association with injectiontreatments applied to a subterranean formation. The injection treatmentsare typically applied to induce fractures in the subterranean formation,and to thereby enhance hydrocarbon productivity of the subterraneanformation. The pressures generated by the stimulation treatment caninduce low-amplitude or low-energy seismic events in the subterraneanformation, and the events can be detected by sensors and collected foranalysis.

DESCRIPTION OF DRAWINGS

FIG. 1A is a schematic diagram of an example well system; FIG. 1B is adiagram of the example computing subsystem 110 of FIG. 1A.

FIG. 2A is a plot showing an example of a boundary calculated frommicroseismic data;

FIG. 2B is another plot showing the example boundary 208 from FIG. 2A.

FIG. 3A is a plot showing an example of a boundary and microseismicdata; FIG. 3B is a plot showing an updated version of the exampleboundary 308 a from FIG. 3A.

FIG. 4A is a plot showing an example of a boundary and microseismicdata; FIG. 4B is a plot showing an updated version of the exampleboundary 408 a from FIG. 4A.

FIG. 5A is a plot showing an example of a boundary and microseismicdata; FIG. 5B is a plot showing inner and outer uncertainty boundariesassociated with the example boundary 508 in FIG. 5A.

FIG. 6 is a plot showing example microseismic event data collected froma multi-stage injection treatment.

FIG. 7 is a plot showing a three-dimensional representation ofoverlapping stimulated reservoir volumes (SRVs) associated withrespective stages of a multi-stage injection treatment.

FIG. 8 is a plot showing a two-dimensional representation of theoverlapping SRVs shown in the plot 700 in FIG. 7.

FIG. 9 is a flow chart showing an example technique for processingmicroseismic data.

FIG. 10 is a flow chart showing an example technique for identifying anSRV from microseismic data.

FIG. 11 is a flow chart showing an example technique for identifyinguncertainty for an SRV calculation.

FIG. 12 is a flow chart showing an example technique for identifyingoverlapping SRVs.

FIG. 13 is a flow chart showing an example technique for calculating SRVin real time.

FIG. 14 is a flow chart showing an example technique for identifyinggeometric properties of SRV for a stimulated subterranean region.

FIG. 15A is a plot showing an example of a boundary and its vertices;FIG. 15B is a plot showing an ellipsoid associated with the exampleboundary 1508 in FIG. 15A.

FIG. 16A is a plot showing an example of a visualization 1600 a ofmicroseismic events, hydraulic fractures, and SRV boundaries; FIG. 16Bis a plot showing another view of the example visualization 1600 a inFIG. 16A.

FIG. 17 is a plot showing example SRV boundaries calculated from examplemicroseismic event data collected from a multi-stage injectiontreatment.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

In some aspects of what is described here, a stimulated reservoir volume(SRV) for a stimulation treatment is approximated and calculated frommicroseismic data. In some instances, an SRV uncertainty, an SRVoverlap, geometric properties of the SRV, or other types of informationare adequately approximated based on calculations from the microseismicdata. In some instances, these or other types of information aredynamically identified and displayed, for example, in a real-timefashion during a stimulation treatment. The stimulation treatment caninclude, for example, an injection treatment, a flow-back treatment, oranother treatment. In some instances, the techniques described here canprovide field engineers or others with a reliable and direct tool tovisualize the stimulated reservoir geometry and treatment fielddevelopment, to evaluate the efficiency of hydraulic fracturingtreatments, to modify or otherwise manage a treatment plan, or toperform other types of analysis or design.

In some instances, the calculated SRV can be proportional to orotherwise indicate the volume of a subterranean region that wasfractured, effectively stimulated, or otherwise affected by astimulation treatment. For example, the calculated SRV may represent thevolume in which fractures or fracture networks were created, dilated, orpropagated by the stimulation treatment. In some instances, SRV canrepresent the volume of a subterranean region that was contacted bytreatment fluid from the stimulation treatment. In some aspects, thecalculated SRV can be obtained based on the volume of a cloud ofmicroseismic events generated by the stimulation treatments. In someimplementations, the calculated SRV can be used to evaluate theefficiency of an injection treatment and to assess treatment wellperformance. In some cases, a more consistent and accurate estimation orprediction of SRV can provide a useful tool for analyzing a stimulatedreservoir.

In some implementations, microseismic data can be collected from astimulation treatment, such as a multi-stage hydraulic fracturingtreatment. Based on locations of the microseismic events, a geometricalrepresentation of the SRV can be constructed, and a quantitativerepresentation of the SRV can be calculated based on the geometricalrepresentation. The geometrical representation can include, for example,a three-dimensional (3D) convex hull or a two-dimensional (2D) convexpolygon enclosing some or all of the microseismic events. Thegeometrical representation can include plots, tables, charts, graphs,coordinates, vector data, maps or other geometrical objects. In someimplementations, in addition to the volume of the SRV for the stimulatedsubterranean region, other geometric properties (e.g., a length, width,height, orientation) of the SRV can be identified based on thegeometrical representation. The geometric properties can be used tocharacterize the stimulated subterranean region. For example, thegeometrical representation can indicate an extension of hydraulicfractures in the stimulated subterranean formation. In some instances, astimulated contact area can be identified, for example, by projecting 3Dmicroseismic events onto a reference plane (e.g., a horizontal plane) orby another technique.

In some instances, due to low-amplitude or low-energy microseismicevents or low signal-to-noise (SNR) measurements, some uncertainty canbe associated with the data for each microseismic event. In some cases,the uncertainty associated with the microseismic events can be used toquantify the uncertainty of the calculated SRV. The uncertainty caninclude, for example, location, moment (e.g., energy or amplitude),time, or another type of uncertainty associated with the microseismicevents. The uncertainty can reflect the accuracy of the SRV estimation.In some cases, the uncertainty can serve as a metric for injectiontreatment evaluation, treatment plan design, or other types of analysis.

In some implementations, for a multi-stage injection treatment, SRV canbe identified for each distinct treatment stage. In some instances, theoverlap in SRV between neighboring or geographically close stages can beextracted from the individual SRV of each stage. A total SRV can bederived for the multi-stage injection treatment based on the SRV foreach stage, while accounting for the overlap. In some instances, theoverlap in SRV between stages indicates fluid connection betweenhydraulic fractures created by each stage, and may imply diversion oftreatment fluid during the hydraulic fracturing process. The extractedSRV overlap and the estimated communication can be used, for example, byfield engineers to control the loss of treatment fluid in real-timefashion, to modify the treatment strategy, or otherwise manage thetreatment plan. In some cases, the efficiency of a stimulation treatmentcan indicate the amount of the reservoir (e.g., the amount of theunfractured reservoir) contacted by a given fracture treatment. In someinstances, the efficiency can be improved or maximized by reducing orminimizing SRV overlap between two adjacent injection stages. Improvingfracturing efficiency via overlap reduction can help reduce costs orprovide other benefits in some instances.

In some implementations, the geophysical geometry of the SRV at eachstage, the overlapping volumes between adjacent stages, the stimulatedcontact area, or a combination of these and other types of informationcan be graphically displayed. The quantity of SRV at each stage, theaccuracy or uncertainty of the SRV calculation, an estimate ofoverlapped volumes, a percentage of the overlapping volumes over the SRVof a treatment stage, or other appropriate quantities can be displayedor otherwise provided, for example, to help field engineers identify theefficiency of the treatment and possible communication between differentstages, or other information.

Generally, the techniques described here can be performed at any time,for example, before, during, or after a treatment or other event. Insome instances, the techniques described here can be implemented in realtime, for example, during a stimulation treatment. Generating orpresenting data in real-time may allow well operators or field engineersto visualize the temporal and spatial evolution of the SRV, dynamicallyidentify the geometry of the SRV and control the development of the SRVto maximize the SRV and production. In some instances, physicalconnection or fluid communication between stimulated regions of multiplestages can be identified in real time and the treatment strategy can beadjusted in real time, for instance, to reduce or avoid loss oftreatment fluid, to improve the efficiency of hydraulic fracturingefforts, or to enhance hydrocarbon productivity. In some instances, thereal-time SRV analysis can be combined with real-time hydraulic fracturemapping, for example, to provide additional information about thehydraulic fracturing treatment.

FIG. 1A is a diagram of an example well system 100 with a computingsubsystem 110. The example well system 100 includes a wellbore 102 in asubterranean region 104 beneath the ground surface 106. The examplewellbore 102 shown in FIG. 1A includes a horizontal wellbore. However, awell system may include any combination of horizontal, vertical, slant,curved, or other wellbore orientations. The well system 100 can includeone or more additional treatment wells, observation wells, or othertypes of wells.

The computing subsystem 110 can include one or more computing devices orsystems located at the wellbore 102, or in other locations. Thecomputing subsystem 110 or any of its components can be located apartfrom the other components shown in FIG. 1A. For example, the computingsubsystem 110 can be located at a data processing center, a computingfacility, or another suitable location. The well system 100 can includeadditional or different features, and the features of the well systemcan be arranged as shown in FIG. 1A or in another configuration.

The example subterranean region 104 may include a reservoir thatcontains hydrocarbon resources, such as oil, natural gas, or others. Forexample, the subterranean region 104 may include all or part of a rockformation (e.g., shale, coal, sandstone, granite, or others) thatcontain natural gas. The subterranean region 104 may include naturallyfractured rock or natural rock formations that are not fractured to anysignificant degree. The subterranean region 104 may include tight gasformations of low permeability rock (e.g., shale, coal, or others).

The example well system 100 shown in FIG. 1A includes an injectionsystem 108. The injection system 108 can be used to perform astimulation treatment that includes, for example, an injection treatmentand a flow back treatment. During an injection treatment, fluid isinjected into the subterranean region 104 through the wellbore 102. Insome instances, the injection treatment fractures part of a rockformation or other materials in the subterranean region 104. In suchexamples, fracturing the rock may increase the surface area of theformation, which may increase the rate at which the formation conductsfluid resources to the wellbore 102.

A fracture treatment can be applied at a single fluid injection locationor at multiple fluid injection locations in a subterranean region, andthe fluid may be injected over a single time period or over multipledifferent time periods. In some instances, a fracture treatment can usemultiple different fluid injection locations in a single wellbore,multiple fluid injection locations in multiple different wellbores, orany suitable combination. Moreover, the fracture treatment can injectfluid through any suitable type of wellbore, such as, for example,vertical wellbores, slant wellbores, horizontal wellbores, curvedwellbores, or any suitable combination of these and others.

The example injection system 108 can inject treatment fluid into thesubterranean region 104 from the wellbore 102. The injection system 108includes instrument trucks 114, pump trucks 116, and an injectiontreatment control subsystem 111. The example injection system 108 mayinclude other features not shown in the figures. The injection system108 may apply injection treatments that include, for example, asingle-stage injection treatment, a multi-stage injection treatment, amini-fracture test treatment, a follow-on fracture treatment, are-fracture treatment, a final fracture treatment, other types offracture treatments, or a combination of these.

The example injection system 108 in FIG. 1A uses multiple treatmentstages or intervals 118 a and 118 b (collectively “stages 118”). Theinjection system 108 may delineate fewer stages or multiple additionalstages beyond the two example stages 118 shown in FIG. 1A. The stages118 may each have one or more perforation clusters 120. A perforationcluster can include one or more perforations 138. Fractures in thesubterranean region 104 can be initiated at or near the perforationclusters 120 or elsewhere. The stages 118 may have different widths, orthe stages 118 may be uniformly distributed along the wellbore 102. Thestages 118 can be distinct, non-overlapping (or overlapping) injectionzones along the wellbore 102. In some instances, each of the multipletreatment stages 118 can be isolated, for example, by packers or othertypes of seals in the wellbore 102. In some instances, each of thestages 118 can be treated individually, for example, in series along theextent of the wellbore 102. The injection system 108 can performidentical, similar, or different injection treatments at differentstages.

The pump trucks 116 can include mobile vehicles, immobile installations,skids, hoses, tubes, fluid tanks, fluid reservoirs, pumps, valves,mixers, or other types of structures and equipment. The example pumptrucks 116 shown in FIG. 1A can supply treatment fluid or othermaterials for the injection treatment. The pump trucks 116 may containmultiple different treatment fluids, proppant materials, or othermaterials for different stages of a stimulation treatment.

The example pump trucks 116 can communicate treatment fluids into thewellbore 102, for example, through a conduit, at or near the level ofthe ground surface 106. The treatment fluids can be communicated throughthe wellbore 102 from the ground surface 106 level by a conduitinstalled in the wellbore 102. The conduit may include casing cementedto the wall of the wellbore 102. In some implementations, all or aportion of the wellbore 102 may be left open, without casing. Theconduit may include a working string, coiled tubing, sectioned pipe, orother types of conduit.

The instrument trucks 114 can include mobile vehicles, immobileinstallations, or other suitable structures. The example instrumenttrucks 114 shown in FIG. 1A include an injection treatment controlsubsystem 111 that controls or monitors the stimulation treatmentapplied by the injection system 108. The communication links 128 mayallow the instrument trucks 114 to communicate with the pump trucks 116,or other equipment at the ground surface 106. Additional communicationlinks may allow the instrument trucks 114 to communicate with sensors ordata collection apparatus in the well system 100, remote systems, otherwell systems, equipment installed in the wellbore 102 or other devicesand equipment.

The example injection treatment control subsystem 111 shown in FIG. 1Acontrols operation of the injection system 108. The injection treatmentcontrol subsystem 111 may include data processing equipment,communication equipment, or other systems that control stimulationtreatments applied to the subterranean region 104 through the wellbore102. The injection treatment control subsystem 111 may include or becommunicably linked to a computing system (e.g., the computing subsystem110) that can calculate, select, or optimize fracture treatmentparameters for initialization, propagation, or opening fractures in thesubterranean region 104. The injection treatment control subsystem 111may receive, generate or modify a stimulation treatment plan (e.g., apumping schedule) that specifies properties of a stimulation treatmentto be applied to the subterranean region 104.

The stimulation treatment, as well as other activities and naturalphenomena, can generate microseismic events in the subterranean region104. In the example shown in FIG. 1A, the injection system 108 hascaused multiple microseismic events 132 during a multi-stage injectiontreatment. A subset 134 of microseismic events are shown inside acircle. In some implementations, the subset 134 of microseismic eventsare events associated with a single treatment stage (e.g., treatmentstage 118 a) of a multi-stage injection treatment. In someimplementations, the subset 134 of microseismic events can be identifiedbased on the time that they occurred, and the subset 134 can be filteredor otherwise modified to exclude outliers or other event points. Thesubset 134 of microseismic events can be selected from a superset ofmicroseismic events based on any suitable criteria. In some cases, thesubset 134 of microseismic events are used to identify an SRV for thestage 118 a or another aspect of an injection treatment.

The microseismic event data can be collected from the subterraneanregion 104. For example, the microseismic data can be collected by oneor more sensors 136 associated with the injection system 108, or themicroseismic data can be collected by other types of systems. Themicroseismic information detected in the well system 100 can includeacoustic signals generated by natural phenomena, acoustic signalsassociated with a stimulation treatment applied through the wellbore102, or other types of signals. For instance, the sensors may detectacoustic signals generated by rock slips, rock movements, rock fracturesor other events in the subterranean region 104. In some instances, thelocations of individual microseismic events can be determined based onthe microseismic data. Microseismic events in the subterranean region104 may occur, for example, along or near induced hydraulic fractures.The microseismic events may be associated with pre-existing naturalfractures or hydraulic fracture planes induced by fracturing activities.

The wellbore 102 shown in FIG. 1A can include sensors 136, microseismicarray, and other equipment that can be used to detect microseismicinformation. The sensors 136 may include geophones or other types oflistening equipment. The sensors 136 can be located at a variety ofpositions in the well system 100. In FIG. 1A, sensors 136 are installedat the surface 106 and beneath the surface 106 (e.g., in an observationwell (not shown)). Additionally or alternatively, sensors may bepositioned in other locations above or below the surface 106, in otherlocations within the wellbore 102, or within another wellbore (e.g.,another treatment well or an observation well). The wellbore 102 mayinclude additional equipment (e.g., working string, packers, casing, orother equipment) not shown in FIG. 1A.

In some cases, all or part of the computing subsystem 110 can becontained in a technical command center at the well site, in a real-timeoperations center at a remote location, in another appropriate location,or any suitable combination of these. The well system 100 and thecomputing subsystem 110 can include or access any suitable communicationinfrastructure. For example, well system 100 can include multipleseparate communication links or a network of interconnectedcommunication links. The communication links can include wired orwireless communications systems. For example, the sensors 136 maycommunicate with the instrument trucks 114 or the computing subsystem110 through wired or wireless links or networks, or the instrumenttrucks 114 may communicate with the computing subsystem 110 throughwired or wireless links or networks. The communication links can includea public data network, a private data network, satellite links,dedicated communication channels, telecommunication links, or anysuitable combination of these and other communication links.

The computing subsystem 110 can analyze microseismic data collected inthe well system 100. For example, the computing subsystem 110 mayanalyze microseismic event data from a stimulation treatment of asubterranean region 104. Microseismic data from a stimulation treatmentcan include data collected before, during, or after fluid injection. Thecomputing subsystem 110 can receive the microseismic data at anysuitable time. In some instances, the computing subsystem 110 receivesthe microseismic data in real time (or substantially in real time)during the fracture treatment. For example, the microseismic data may besent to the computing subsystem 110 immediately upon detection by thesensors 136. In some instances, the computing subsystem 110 receivessome or all of the microseismic data after the fracture treatment hasbeen completed. The computing subsystem 110 can receive the microseismicdata in any suitable format. For example, the computing subsystem 110can receive the microseismic data in a format produced by microseismicsensors or detectors, or the computing subsystem 110 can receive themicroseismic data after the microseismic data has been formatted,packaged, or otherwise processed. The computing subsystem 110 canreceive the microseismic data, for example, by a wired or wirelesscommunication link, by a wired or wireless network, or by one or moredisks or other tangible media.

The computing subsystem 110 can perform, for example, fracture mappingand matching based on collected microseismic event data to identifyfracture orientation trends and extract fracture networkcharacteristics. The characteristics may include fracture orientation(e.g., azimuth and dip angle), fracture size (e.g., length, height,surface area), fracture spacing, fracture complexity, stimulatedreservoir volume (SRV), or another property. In some implementations,the computing subsystem 110 can identify SRV for a stimulation treatmentapplied to the subterranean region 104, calculate an uncertainty of theSRV calculation, identify overlapping volume of SRV between stages of astimulation treatment, or other information. The computing subsystem 110can perform additional or different operations.

In one aspect of operation, the injection system 108 can perform aninjection treatment, for example, by injecting fluid into thesubterranean region 104 through the wellbore 102. The injectiontreatment can be, for example, a multi-stage injection treatment wherean individual injection treatment is performed during each stage. Theinjection treatment can induce microseismic events in the subterraneanregion 104. Sensors (e.g., the sensors 136) or other detecting equipmentin the well system 100 can detect the microseismic events, and collectand transmit the microseismic event data, for example, to the computingsubsystem 110. The computing subsystem 110 can receive and analyze themicroseismic event data. For instance, the computing subsystem 110 mayidentify an SRV or other data for the injection treatment based on themicroseismic data. The SRV data may be computed for an individual stageor for the multi-stage treatment as a whole. In some instances, thecomputed SRV data can be presented to well operators, field engineers,or others to visualize and analyze the temporal and spatial evolution ofthe SRV. In some implementations, the microseismic event data can becollected, communicated, and analyzed in real time during an injectiontreatment. In some implementations, the computed SRV data can beprovided to the injection treatment control subsystem 111. A current ora prospective treatment strategy can be adjusted or otherwise managedbased on the computed SRV data, for example, to improve the efficiencyof the injection treatment.

Some of the techniques and operations described here may be implementedby a computing subsystem configured to provide the functionalitydescribed. In various embodiments, a computing system may include any ofvarious types of devices, including, but not limited to, personalcomputer systems, desktop computers, laptops, notebooks, mainframecomputer systems, handheld computers, workstations, tablets, applicationservers, storage devices, computing clusters, or any type of computingor electronic device.

FIG. 1B is a diagram of the example computing subsystem 110 of FIG. 1A.The example computing subsystem 110 can be located at or near one ormore wells of the well system 100 or at a remote location. All or partof the computing subsystem 110 may operate independent of the wellsystem 100 or independent of any of the other components shown in FIG.1A. The example computing subsystem 110 includes a memory 150, aprocessor 160, and input/output controllers 170 communicably coupled bya bus 165. The memory 150 can include, for example, a random accessmemory (RAM), a storage device (e.g., a writable read-only memory (ROM)or others), a hard disk, or another type of storage medium. Thecomputing subsystem 110 can be preprogrammed or it can be programmed(and reprogrammed) by loading a program from another source (e.g., froma CD-ROM, from another computer device through a data network, or inanother manner). In some examples, the input/output controller 170 iscoupled to input/output devices (e.g., a monitor 175, a mouse, akeyboard, or other input/output devices) and to a communication link180. The input/output devices receive and transmit data in analog ordigital form over communication links such as a serial link, a wirelesslink (e.g., infrared, radio frequency, or others), a parallel link, oranother type of link.

The communication link 180 can include any type of communicationchannel, connector, data communication network, or other link. Forexample, the communication link 180 can include a wireless or a wirednetwork, a Local Area Network (LAN), a Wide Area Network (WAN), aprivate network, a public network (such as the Internet), a WiFinetwork, a network that includes a satellite link, or another type ofdata communication network.

The memory 150 can store instructions (e.g., computer code) associatedwith an operating system, computer applications, and other resources.The memory 150 can also store application data and data objects that canbe interpreted by one or more applications or virtual machines runningon the computing subsystem 110. As shown in FIG. 1B, the example memory150 includes microseismic data 151, geological data 152, other data 155,and applications 158. In some implementations, a memory of a computingdevice includes additional or different data, applications, models, orother information.

The microseismic data 151 can include information on microseismic eventsin a subterranean area. For example, the microseismic data 151 caninclude information based on acoustic data detected at the wellbore 102,at the surface 106, or at other locations. The microseismic data 151 caninclude information collected by sensors 136. In some cases, themicroseismic data 151 includes information that has been combined withother data, reformatted, or otherwise processed. The microseismic eventdata may include any suitable information relating to microseismicevents (e.g., locations, times, magnitudes, moments, uncertainties,etc.). The microseismic event data can include data collected from oneor more stimulation treatments, which may include data collected before,during, or after a fluid injection.

The geological data 152 can include information on the geologicalproperties of the subterranean zone 104. For example, the geologicaldata 152 may include information on the wellbore 102, or information onother attributes of the subterranean region 104. In some cases, thegeological data 152 includes information on the lithology, fluidcontent, stress profile, pressure profile, spatial extent, or otherattributes of one or more rock formations in the subterranean area. Thegeological data 152 can include information collected from well logs,rock samples, outcroppings, microseismic imaging, or other data sources.

The applications 158 can include software applications, scripts,programs, functions, executables, or other modules that are interpretedor executed by the processor 160. The applications 158 may includemachine-readable instructions for performing one or more of theoperations related to FIGS. 2-13. The applications 158 may includemachine-readable instructions for generating a user interface or a plot,for example, illustrating fracture geometry (e.g., length, width,spacing, orientation, etc.), geometric representations of SRV, SRVoverlap, SRV uncertainty, etc. The applications 158 can obtain inputdata, such as treatment data, geological data, microseismic data, orother types of input data, from the memory 150, from another localsource, or from one or more remote sources (e.g., via the communicationlink 180). The applications 158 can generate output data and store theoutput data in the memory 150, in another local medium, or in one ormore remote devices (e.g., by sending the output data via thecommunication link 180).

The processor 160 can execute instructions, for example, to generateoutput data based on data inputs. For example, the processor 160 can runthe applications 158 by executing or interpreting the software, scripts,programs, functions, executables, or other modules contained in theapplications 158. The processor 160 may perform one or more of theoperations related to FIGS. 2-13. The input data received by theprocessor 160 or the output data generated by the processor 160 caninclude any of the microseismic data 151, the geological data 152, orthe other data 155.

An example process for analyzing the SRV based on microseismic eventdata is represented in the plots and corresponding description of FIGS.2A-5B. In some implementations, SRV can be represented geometrically inone dimension, two dimensions, three dimensions, or anotherrepresentation. The geometrical representation can be of any appropriateshape, for example, including a rectangle, a circle, a polygon, asphere, an ellipsoid, a polyhedron, a combination of them, etc. Thegeometrical representation can have any suitable property (e.g.,regular, irregular, closed, open, convex, concave, non-convex,non-concave, etc.). As an example, the geometrical representation caninclude a boundary (e.g., a surface, a 3D convex hull, a 2D polyhedron,etc.) enclosing multiple microseismic event locations.

In some instances, computing a boundary based on microseismic event datacan include filtering the collected microseismic event data to identifya selected subset of microseismic events. In some implementations, themicroseismic events can be filtered based on the time, location,magnitude, moment, or another attributes of the microseismic events. Insome instances, the microseismic events can be filtered according totheir associated treatment stage. In some instances, the microseismicevents can be filtered to exclude outliers, low density events, or acombination of these and other events. The selected subset ofmicroseismic events can be used to calculate the boundary to representthe SRV for a stimulation treatment.

In some implementations, computing the boundary can include calculatingan initial boundary based on multiple microseismic events (e.g., eventsat extreme locations) as shown in FIGS. 2A, 2B. The calculated boundarycan be iteratively expanded based on the selected subset of microseismicevents that reside outside the boundary, for example, as shown in FIGS.3A, 3B and 4A, 4B. As an example, a facet expansion operation may beperformed that includes identifying facet expansion groups from theselected subset of microseismic events residing outside the boundary,and expanding facets of the calculated boundary to enclose microseismicevents in the expansion groups. In some implementations, the boundaryexpansion operation can be performed iteratively and result in aboundary that encloses (i.e., contains or intersects) all the events inthe selected subset while some other events (e.g., the filteredoutliers, low density events, etc.) may reside outside the boundary. Insome implementations, the boundary can be refined, for example, based onfurther filtering, smoothing vertices, edges, etc., as shown in FIG. 5A.The boundary can be used to identify an SRV for a stimulation treatment.For instance, the internal volume of the boundary can be calculated asthe SRV for the stimulation treatment.

FIG. 2A is a plot 200 a showing an example of a boundary 208 calculatedfrom locations of microseismic events 206. FIG. 2B is another plot 200 bshowing the example boundary 208 from FIG. 2A. In the illustrated plots200 a-b, the example boundary 208 is an example of a 3D convex hull. Theboundary can be another type of geometrical object.

In some instances, the microseismic events 206 can be associated with asingle stage of a multi-stage injection treatment. For example, whenthere are n microseismic events detected during a stage of a hydraulicfracture treatment, each microseismic event can be represented as alocation (x_(i), y_(i), z_(i)), 1≦i≦n, corresponding uncertainty andpossibly other parameters. The microseismic events 206 may be located inthe production pay zone, contributing to the SRV, or other locations.

The example plot 200 a shows the SRV in a three-dimensional rectilinearcoordinate system. The coordinate system is represented by the verticalaxis 204 a and two horizontal axes 204 b and 204 c. In the example plot200 a, the vertical axis 204 a represents a range of depths in asubterranean zone; the horizontal axis 204 b represents a range ofEast-West coordinates; and the horizontal axis 204 c represents a rangeof North-South coordinates (all in units of feet). In someimplementations, the data represented in FIG. 2A can be represented byanother type of geometrical object in any suitable coordinate system(e.g., spherical coordinates, rectangular coordinates, etc.) or domain.Although the plots show distance information in units of feet, otherunits can be used. Calculations can be performed and information can bedisplayed in metric units (mks, cgs, or another system), standard units,or another unit system. In some cases, an algorithm can use metricunits, standard units, or convert among unit systems.

In some implementations, before computing an SRV boundary, outliersamong the microseismic data can be identified and removed. The outlierscan include, for example, statistical outliers, deterministic outliers,or another type of outlier. In some implementations, outliers cancontaminate the SRV estimation, for example, when the outliers includereflections of events unrelated to the stimulation treatment. Excludingthe outliers can reduce or eliminate interference from other unrelatedevents to the SRV identification and can lead to a more accurateestimation of the SRV for the stimulation treatment. In some instances,outliers deviate markedly from other events, and can be isolated pointsbased on a threshold, a statistical deviation, or another criterion. Forexample, deterministic outliers may have an outrageous location, moment,or any other attribute and may belong to another wellbore or anotherirrelevant treatment. The deterministic outliers can be identified andcleared, for example, by removing microseismic events with a certainattribute exceeding a threshold. In some implementations, outliers canbe detected based on statistical properties of the microseismic dataset. For example, in some cases, statistical outliers includemicroseismic events whose distance from an average location of themicroseismic events is larger than a threshold. The average location canbe, for example, the mean value of the locations (x_(i), y_(i), z_(i)),1≦i≦k, of the microseismic events in the data set. The threshold can be,for example, the sum of the computed mean value and three (or two, four,etc.) times the standard deviation. In such cases, an example techniqueto identify the outliers can include calculating the mean and standarddeviation for the set of the microseismic events. Additional ordifferent criteria or techniques can be used to detect outliers. FIG. 5Ashows five example outliers 555 lying outside an example boundary 508.

In some examples, after removing outliers from the microseismic data, aninitial boundary can be calculated based on the remaining microseismicevents. In some implementations, the initial boundary can be calculatedbased on identifying events at extreme locations. The events at extremelocations can include events with the minimum and maximum coordinates(e.g., the minimum x-coordinate and the maximum x-coordinate, theminimum y-coordinate and the maximum y-coordinate, and the minimumz-coordinate and the maximum z-coordinate). In the example plot 200 a,the axes 204 a, 204 b, and 204 c can be the z-coordinate, x-coordinate,and the y-coordinate, respectively. Six events 210 a-210 f at extremelocations can be identified and regarded as vertices of an initialboundary. The example boundary 208 is constructed based on the sixvertices 210 a-210 f. The initial boundary 208 has eight triangularfacets 220 a-220 h, as shown in FIG. 2B, and the initial boundary 208can be expanded to enclose additional microseismic events. In somecases, the facets can be expanded independent of the events (shown asopen circles) lying inside the initial boundary 208. The events (shownas solid circles) lying outside the initial boundary 208 can be assignedto eight facet expansion groups. In the example shown, each expansiongroup is associated with one of the eight facets 220 a-220 h. FIG. 2Bshows four top triangular facets 220 a-220 d of the initial boundary 208each with a respective arrow. The initial boundary 208 can be expandedto enclose events in the facet expansion groups, for example, accordingto a facet expansion operation.

An example facet expansion operation is described as follows. In someimplementations, the average location of the six vertices 210 a-210 fcan be calculated and denoted P₀ (x₀, y₀, z₀). P₀ lies inside theinitial boundary 208. A triangular facet containing three non-collinearvertices (x₁, y₁, z₁), (x₂, y₂, z₂) and (x₃, y₃, z₃) can be described byequations (1-a)-(1-e):

$\begin{matrix}{{{{ax} + {by} + c + d} = 0}{where}} & \left( {1\text{-}a} \right) \\{{a = {\begin{matrix}1 & y_{1} & z_{1} \\1 & y_{2} & z_{2} \\1 & y_{3} & z_{3}\end{matrix}}},} & \left( {1\text{-}b} \right) \\{{b = {\begin{matrix}x_{1} & 1 & z_{1} \\x_{2} & 1 & z_{2} \\x_{3} & 2 & z_{3}\end{matrix}}},} & \left( {1\text{-}c} \right) \\{{c = {\begin{matrix}x_{1} & y_{1} & 1 \\x_{2} & y_{2} & 1 \\x_{3} & y_{3} & 1\end{matrix}}},} & \left( {1\text{-}d} \right) \\{d = {- {{\begin{matrix}x_{1} & y_{1} & z_{1} \\x_{2} & y_{2} & z_{2} \\x_{3} & y_{3} & z_{3}\end{matrix}}.}}} & \left( {1\text{-}e} \right)\end{matrix}$A facet may be described in another manner. The normal distance from theaverage location P₀ (x₀, y₀, z₀) to the facet can be given by

$d_{0} = {- \frac{{ax}_{0} + {by}_{0} + {cz}_{0} + d}{\sqrt{a^{2} + b^{2} + c^{2}}}}$and the normal distance from an event P_(i) (x_(i), y_(i), z_(i)) to thefacet can be given by

$d_{i} = {- {\frac{{ax}_{i} + {by}_{i} + {cz}_{i} + d}{\sqrt{a^{2} + b^{2} + c^{2}}}.}}$These distances can have a sign (±) if these events do not exactly lieon the facet. For example, if d₀*d_(i) is positive, then P₀ and P_(i)lie on the same side of the facet; if d₀*d_(i) is negative, then P₀ andP_(i) lie on the opposite sides of the facet. In some implementations,the events satisfying the condition d₀*d_(i)<0 can be identified as afacet expansion group associated with the facet. In some cases, theevents in the facet expansion group associated with a facet lie on thesame side of the facet. In the illustrated example of FIG. 2B, eightexpansion groups can be associated with the eight facets 220 a-220 h,respectively. In some implementations, the assignment of an event to anexpansion group is not a one-to-one mapping. For example, one event maybe assigned to more than one group, and two or more groups may intersecteach other and share one or more common events.

In some instances, two or more of the six events 210 a-210 f at extremelocations may collapse with each other. As such, the initial convex setmay have less than eight (e.g., six or four) facets. A similar facetexpansion process can apply to these cases without affecting the finalresult.

For each expansion group associated with a facet, the facet expansionoperation can modify the facet to enclose the microseismic events in theexpansion group. The operation can include identifying an event that hasthe maximum distance from its associated facet. The event with themaximum distance from the facet can be a vertex of an updated version ofthe boundary. In some instances, such an event may be shared by otherexpansion groups, and the operations can be modified accordingly. FIGS.3A and 3B are plots showing example boundaries and microseismic eventswhen the event with the maximum absolute distance from its associatedfacet only belongs to one expansion group. FIGS. 4A and 4B are plotsshowing example boundaries and microseismic events when the event withthe maximum distance from its associated facet is shared by multipleexpansion groups.

FIG. 3A is a plot 300 a showing an example of a boundary 308 a andmicroseismic data. As illustrated, the example boundary 308 a is a 3Dconvex set, and an example expansion group associated with a facet 320 aincludes three microseismic events 306 a-c. Among three events, themicroseismic event 306 a has the maximum distance from the associatedfacet 320 a. In the situation, the event 306 a belongs only to thesubset associated with the facet 320 a. The boundary 308 a can beupdated to enclose the expansion group associated with the facet 320 a.

FIG. 3B is a plot 300 b showing an example updated boundary 308 b, whichis an updated version of the boundary 308 a shown in FIG. 3A. Theupdated boundary can be generated based on the expansion groupassociated with the facet 320 a in FIG. 3A. In an example process, theevent 306 a can be selected as a new vertex of the updated boundary 308b. The original facet 320 a of the boundary 308 a can be deleted andthree new triangular facets 320 b-d can be created. Each of the newtriangular facets 320 b-d has the event 306 a and another two verticesof the three vertices 306 e-g of the facet 302 a as its vertices. Theselection of the event 306 a with the maximum absolute distance canguarantee that the new facets 320 b-d along with the other seven facetsof the boundary 308 a make up a convex set.

In the example plot 300 b, the three new triangular facets 320 b-d andthe original triangular facet 320 a make up a tetrahedron 330. Thoseevents inside the tetrahedron 330 can be removed from the expansiongroup. Applying a facet expansion operation on the events outside thetetrahedron 330 can create three new expansion groups associated witheach of the three new facets 320 b-d. In some instances, since theorientations of new triangular facets 320 b-d can be different from theoriginal facet 320 a, events associated with neighbors of the facet 320a may also be expanded to the three new expansion groups.

FIG. 4A is a plot 400 a showing an example of a boundary 408 a andmicroseismic data; FIG. 4B is a plot 400 b showing an updated version ofthe example boundary 408 a from FIG. 4A. In the example plot 400 a ofFIG. 4A, the example boundary 408 a is a 3D convex set, and an exampleexpansion group associated with a facet 420 a includes multiplemicroseismic events. Among the multiple microseismic events, the event406 a has the maximum distance from its associated facet 420 a. In thesituation shown in FIG. 4A, the event 406 a is shared by two otherexpansion groups associated with facets 420 b and 420 c respectively, inaddition to the group associated with facet 420 a. In some instances, toidentify a facet with which an event (e.g., event 406 a) is associated,one can image that the event 406 a is a small light bulb. The facets(e.g., facets 420 a-c) that can be illuminated by the event 406 a (orthe facets that are visible to the location at the event 406 a) can befacets associated with the event 406 a. Additional or differenttechniques can be used to identify facets that are associated with theevent 406 a. The boundary 408 a can be updated to enclose the expansiongroups that include the event 406 a.

FIG. 4B is a plot 400 b showing an example updated 3D boundary 408 bbased on the 3D boundary 408 a and the subsets that include the event406 a in FIG. 4A. In an example process, the internal edges shared byany two adjacent facets of the facets 420 a-c can be erased. Theexternal edges form a boundary 440 of the facets 420 a-c. The threefacets 420 a-c of the boundary 408 a can be deleted and new triangularfacets 420 d-h can be created. Each of the five new facets 420 d-h hasthe event 406 a and any two adjacent vertices on the boundary 440 as itsvertices. In some instances, selecting the event 406 a with the maximumdistance can guarantee that the new facets 420 d-h along with the restof the facets of the boundary 408 a make up a convex set.

In the example plot 400 b, the old facets 420 a-c and new facets 420 d-hform a new polyhedron 430. The events inside the polyhedron 430 can beremoved from the expansion groups. The facet expansion operationperformed based on the events outside the polyhedron 430 can create fivenew expansion groups associated with the five new facets 420 d-h,respectively. In some implementations, the events in these new groupsmay come not only from the events associated with the facets 420 a-c butalso from the events associated with the other facets that neighbor thefacets 420 a-c.

In the example operations described with respect to FIGS. 2A-4B, thegeometric object plotted is a convex set. In some implementations, thecreated structure is not convex, and it can be another shape. Theoperations can be repeated based on expansion groups until there are noevents in any of the groups. Then a final boundary can be obtained andits facets form the boundary of the final boundary. During the recurrentoperations, events inside the created structure can be excluded, thusthe computational complexity can be the order n log(n) where n is thenumber of input microseismic events and the algorithm can be implementedwith a fast computational performance.

In some implementations, a calculated boundary can be refined, forexample, by filtering out low event density points. For a given event,an event density can be calculated, for example, based on the number ofevents per unit volume about the event, based on the average distance tonearest neighbor events, or based on other information. In someinstances, a boundary may have lower event density at its vertices thanother places inside the boundary. To obtain more accurate SRV, theevents at vertices whose event density is less than a threshold (aparameter) can be removed. The same operation as described above can beused to construct a new boundary based on the updated event data toimprove the SRV estimation. In some implementations, the refinement ofthe calculated boundary can be applied to the initial boundary, thefinal boundary, an intermediate boundary, or at any appropriate time.

FIG. 5A is a plot 500 a showing an example of a boundary 508 andmicroseismic data. The example boundary 508 is a 3D convex hull. In someinstances, the boundary 508 can be constructed based on an updated eventdata set of 581 microseismic events. In this example, the updated eventdata set does not include two low density events 565 and five outliers555. The example boundary 508 a has 43 vertices and 82 triangularfacets. FIG. 5A also shows a wellbore 550 and perforation clusters 560.

The volume of the boundary 508 can be calculated to get the SRV. As anexample technique, the center of the boundary 508 can be computed. Thecenter can be, for example, the average location of the vertices.Associated with each facet of the boundary 508, a tetrahedron can beconstructed. One vertex of the tetrahedron can be the center and theother three vertices can be three vertices of the facet. The volume of atetrahedron is one-third of the product of the area of the facet and thedistance from the center to the facet. The SRV can be the sum of thetetrahedrons' volumes. For example, the SRV in FIG. 5A is 2.77 (10)⁸cubic feet (ft³). Additional or different techniques can be used tocompute SRV based on the constructed boundary.

In some implementations, a boundary constructed based on locations ofmicroseismic data can be associated with an uncertainty. For example,some or all of the microseismic events may have the low-amplitude orlow-energy (e.g., with Richter magnitude of less than three), and themeasurement location uncertainty can affect the computation of thesurface associated with the events' location. While acquiringmicroseismic events, sensor distribution, data quality, observationaldistance, underlying velocity model, an applied localization algorithm,or a combination of these and other factors can affect the accuracy of ameasured location of a microseismic event. In some instances, the eventlocation can have azimuth uncertainty relative to an observation well,distance uncertainty relative to the observation well, or depthuncertainty.

In some instances, three or more uncertainty quantities (event's azimuthuncertainty, distance uncertainty, and depth uncertainty) can be applieddirectly to the constructed boundary. To translate these locationuncertainties to the boundary's uncertainty, an example technique is toapproximate an individual event's 3D uncertainty space by a ball withradius r, given by equation (2):4/3πr ³=(azimuth uncertainty)* . . . (distance uncertainty)*(depthuncertainty)  (2).The approximation can preserve the volume of uncertainty space. In somecontext, the uncertainty quantity, r, of an individual event is muchsmaller than the length of any of the facets' edges. Additional ordifferent techniques can be used to describe and quantify theuncertainty of the microseismic event.

One example technique to measure the SRV uncertainty can includeconstructing an inner and an outer alternative boundaries based on theevents' uncertainty quantity r. For example, the center of a convex hullcan be denoted as P₀ (x₀, y₀, z₀). For each vertex P (x_(p), y_(p),z_(p)) of the convex hull, an interior projection (or “shrink”) point onthe segment P₀P and an exterior projection (or “extent”) point on theextension of the line P₀P can be found. If the length of the segment P₀Pis L, the coordinate components of the interior point can be given by:

$\begin{matrix}{x = {x_{0} + {\frac{L - r}{L}\left( {x_{p} - x_{0}} \right)}}} & \left( {3\text{-}a} \right) \\{y = {y_{0} + {\frac{L - r}{L}\left( {y_{p} - y_{0}} \right)}}} & \left( {3\text{-}b} \right) \\{{z = {z_{0} + {\frac{L - r}{L}\left( {z_{p} - z_{0}} \right)}}},} & \left( {3\text{-}c} \right)\end{matrix}$and the components of the exterior point can be given by:

$\begin{matrix}{x = {x_{0} + {\frac{L + r}{L}\left( {x_{p} - x_{0}} \right)}}} & \left( {4\text{-}a} \right) \\{y = {y_{0} + {\frac{L + r}{L}\left( {y_{p} - y_{0}} \right)}}} & \left( {4\text{-}b} \right) \\{{z = {z_{0} + {\frac{L + r}{L}\left( {z_{p} - z_{0}} \right)}}},} & \left( {4\text{-}c} \right)\end{matrix}$where r is the uncertainty radius of the given event at the vertex. Someor all of the exterior points can be used to construct an outeruncertainty boundary; some or all of the interior points can be used toconstruct an inner uncertainty boundary. The volume difference betweenthese two uncertainty boundaries can be used as a measure of the SRVuncertainty. In some implementations, additional or different inner orouter bounds can be identified based on the microseismic events and theSRV uncertainty can be determined in another manner based on otherinformation.

FIG. 5B is a plot showing an inner uncertainty boundary 507 and an outeruncertainty boundary 509 associated with the example boundary 508 inFIG. 5A. The example inner and outer boundaries are illustrated as aninner boundary 507 and an outer boundary 509, respectively. Theboundaries 507, 508, and 509 are defined in a common spatial domain withaxes 504 a-c. To better visualize the microseismic events inside theboundary 508, the top 12 facets are open (removed) in the figure. In theillustrated plot 500 b, the SRV uncertainty is 1.873 (10)⁷ cubic (ft³),about 6.7% of the calculated SRV.

In some instances, a multi-stage injection treatment can be applied to asubterranean region. The multi-stage injection treatment may includeindividually treated stages and microseismic event data can be obtainedfor each stage. In some implementations, the example process describedabove for analyzing the SRV can be applied to the microseismic eventdata associated with each individual stage. For example, themicroseismic event data associated with each individual stage can befiltered (e.g., to exclude outliers, low density events, etc.) andanalyzed (e.g., for computing a boundary to enclose a subset of themicroseismic events associated with each stage, identifying an SRV foreach stage based on the computed boundary, etc.). In some instances,physical connection or fluid communication may exist between stimulatedregions of multiple stages. The SRVs for two or more stages may overlapwith each other. The overlapping volume of SRVs and the overlap ofboundaries can be identified based on the microseismic event data. Insome implementations, a total SRV for the multi-stage injectiontreatment can be identified based on the SRV for each stage and theoverlapping volume between stages.

FIG. 6 is a plot 600 showing example microseismic event data collectedfrom a multi-stage hydraulic fracturing treatment. In someimplementations, a multi-stage hydraulic fracturing strategy can be usedin long horizontal wells to improve stimulated reservoir volume.Microseismic event data can be collected at each stage of themulti-stage fracturing treatment. The example plot 600 shows a subset610 that includes 770 microseismic events (shown as circles) at stage 1,a subset 620 that includes 1201 events (shown as squares) at stage 2, asubset 630 that includes 476 events (shown as triangles) at stage 3, anda subset 640 that includes 424 events (shown as diamonds) at stage 4. Awellbore 650 and perforation clusters 660 for the example four-stagehydraulic fracturing treatment are also shown in FIG. 6.

FIG. 7 is a plot 700 showing a three-dimensional (3D) representation ofoverlapping SRVs associated with distinct stages of a multi-stageinjection treatment. In the illustrated plot 700, the boundaries 710,720, 730, and 740 are constructed based on the events subsets 610, 620,630, and 640 in FIG. 6, respectively. The boundaries can be constructedaccording to the example technique described with respect to FIGS.2A-5B, or based on another technique. In the example shown in FIG. 7,the SRVs associated with the four stages are 7.83 (10)⁸, 9.56 (10)⁸,7.74 (10)⁸ and 8.73 (10)⁸ cubic feet (ft³) respectively.

In some instances, the total SRV for a multi-stage hydraulic fracturingtreatment is not directly obtained from the individual SRV quantities ofeach stage. For example, there may be overlapping volumes between thestages. FIG. 7 shows boundaries 715, 725, and 735 of SRV overlap regionsbetween stage 1 and stage 2, stage 2 and stage 3, and stage 3 and stage4, respectively. In some cases, in addition to neighboring stages,geographically close stages can also overlap or otherwise affect eachother. For example, stage 1 and stage 4 may overlap with or otherwiseinfluence each other. In some implementations, the overlapped volumesindicate possible fluid communication between the stages during thehydraulic fracturing process. Such communications may include thediversion of treatment fluid and may decrease the efficiency of anindividual hydraulic fracturing treatment.

An example process for approximating or otherwise identifyingoverlapping volumes between treatment stages is described as follows. Insome implementations, a first phase of the process can includeidentifying microseismic events shared by two stages. Such events lieinside boundaries of both stages and thus are inside the overlappingvolume. For example, to determine the SRV overlap 715 between stage 1and stage 2 in FIG. 7, the events at stage 1 that also lie inside theboundary 720 of stage 2 can be identified. In some implementations, allevents enclosed by the boundary 710 of stage 1 can be scanned. For eachevent at stage 1, the facets of the boundary 720 of stage 2 can bescanned. For each facet of the boundary 720, whether the event and thecenter of the boundary 720 lie on the same side of the facet can bedetermined. In some instances, such a determination can be made byassessing whether a product of their respective distances to the facetis positive. If positive, the event and the center are on the same side;if negative, the event and the center are on opposite sides. In somecases, if the event and the center lie on the same side of eachconsidered facet for all the facets of the boundary 720, the event canbe identified as being shared by the two stages. Similarly, the aboveprocess can be applied to identify the events at stage 2 which also lieinside the boundary 710 of stage 1. After this phase, a set of eventscommonly shared by the two stages can be found.

In some implementations, a second phase of the process can includeidentifying points intersected by a facet of a boundary created at onestage and an edge of a boundary created at another stage. As an example,intersected points where the facet belongs to the boundary 710 of stage1 and the edge belongs to the boundary 720 of stage 2 can be identified.Specifically, facets of the boundary 710 can be identified among whosethree vertices, one of them belongs to the event set identified in thefirst phase and one of them does not belong to the event set. Theconditions can be sufficient for the facets to intersect with theboundary 720. For each such facet, whether there is an edge of theboundary 720 traversing the facet can be determined. In some instances,it can be determined whether one end of the edge belongs to the eventset identified in the first phase and another end does not belong to theidentified event set; or it can be determined that the intersected pointlies inside the facet. Mathematically, the edge can be given by:x=x _(p) +t(x _(Q) −x _(p)),  (5-a)y=y _(P) +t(y _(Q) −y _(p)),  (5-b)z=z _(p) +t(z _(Q) −z _(p)),  (5-c)where 0<t<1, and where P (x_(p), y_(p), z_(p)) and Q (x_(Q), y_(Q),z_(Q)) are two ends of the edge. Substituting the equations (5-a),(5-b), and (5-c) into equation (1) can yield the parameter t, andplugging t into equation (5-a), (5-b), and (5-c) can obtain theintersected point. If for all edges of the facet, the intersected pointlies on the same side as the center of the facet, the point can beidentified as residing in the overlapping volume. Similarly, the aboveprocess can be applied to identify points that are intersected by afacet belonging to the boundary 720 of stage 2 and an edge belonging tothe boundary 710 of stage 1.

In some implementations, a third phase of the process can includecalculating a geometrical object (e.g., a convex hull or another type ofobject) based on the microseismic events identified in the first phaseand intersected points found in the second phase. The boundary can becalculated according to the example technique described with respect toFIGS. 2A-5B, or can be calculated in another manner. The boundary canrepresent the overlapping volume between two stages. As shown on the toparea of FIG. 7, the boundaries 715, 725, and 735 are the SRV overlapsbetween two adjacent stages among the four stages. The volumes of theseoverlapping parts are 8.56 (10)⁷, 9.09 (10)⁷ and 4.16 (10)⁸ cubic feet(ft³), occupying 9.0%, 11.7% and 47.7% of SRVs of stage 2, stage 3 andstage 4, respectively. The overlapping volumes among stage 3 and its twoadjacent stages (stage 2 and stage 4) is 5.07 (10)⁸ ft³, occupying 65.5%of SRV of stage 3.

The total SRV for a multi-stage hydraulic fracturing treatment can becalculated based on the overlapping volume. For example, the total SRVfor a two-stage treatment can be calculated by equation (6):Total SRV(stage1∪stage2)=SRV(stage1)+SRV(stage2)−SRV(stage1∩stage2)  (6)

Generally, the total SRV for a m-stage hydraulic fracturing treatmentcan be, for example, given by equation (7):

${{Total}\mspace{14mu}{{SRV}\left( {\overset{m}{\bigcup\limits_{i = 1}}{{stage}(i)}} \right)}} = {{\sum\limits_{i = 1}^{m}\;{{SRV}\left( {{stage}(i)} \right)}} - {\sum\limits_{i > j}\;{{SRV}\left( {{{stage}(i)}\bigcap{{stage}(j)}} \right)}} + {\sum\limits_{i > j > k}\;{{SRV}\left( {{{stage}(i)}\bigcap{{stage}(j)}\bigcap{{stage}(k)}} \right)}} - \ldots + {\left( {- 1} \right)^{m}{{SRV}\left( {\overset{m}{\bigcap\limits_{i = 1}}{{stage}(i)}} \right)}}}$In the example illustrated in FIG. 7, the total volume for themulti-stage treatment is 2.79 (10)⁹ (ft³). In some implementations, thetotal SRV can be calculated according to a variation of equation (6) or(7), or in another manner.

In some implementations, a stimulated subterranean area and extension ofhydraulic fractures can be determined based on microseismic event data.For instance, the stimulated area contacting a production pay zone canbe determined by projecting 3D microseismic events onto a referenceplane. For example, a reference plane can be given by ax+by+cz+d=0. Anexample reference plane can be a horizontal plane. Based on the planeequation, the plane orientation angles, strike θ and dip φ, can be, forexample, given by equations (8) and (9):

$\begin{matrix}{{\theta = {\arctan\frac{b}{a}}},} & (8) \\{\varphi = {\arctan{\frac{\sqrt{a^{2} + b^{2}}}{c}.}}} & (9)\end{matrix}$For a given treatment stage, after filtering the events (e.g., excludingoutliers and events with low density), the remaining events can beprojected onto the reference plane, for example, by following lineartransformation

$\begin{matrix}{\begin{bmatrix}s \\t \\u\end{bmatrix} = {\begin{bmatrix}{\cos\;{\theta cos}\;\phi} & {\sin\;\theta\;\cos\;\phi} & {{- \sin}\;\phi} \\{{- \sin}\;\theta} & {\cos\;\theta} & 0 \\{\cos\;\theta\;\sin\;\phi} & {\sin\;\theta\;\sin\;\phi} & {\cos\;\phi}\end{bmatrix}\begin{bmatrix}{x - X_{0}} \\{y - Y_{0}} \\{z - Z_{0}}\end{bmatrix}}} & (10)\end{matrix}$where (X₀, Y₀, Z₀) is a point on the reference plane. Note that theselection of the point (X₀, Y₀, Z₀) does not affect results. The aboveequations (8)-(10) can transform an event's 3D location (x, y, z) to theplane coordinates (s, t, u), where actually the u-component is zero. Insome implementations, the u coordinate component can be ignored and onlythe (s, t) coordinates are taken in the following calculation. In someinstances, the x-y coordinates can be used to represent the s-tcoordinates, i.e., the locations of these projected events can beexpressed as (x, y) in the x-y coordinates.

FIG. 8 is a plot 800 showing a two-dimensional (2D) projection ofmicroseismic events of a multi-stage injection treatment and exampletwo-dimensional geometrical representations of stimulated contact areas.In the illustrated example, four sets of projected microseismic events810, 820, 830, and 840 can be obtained by projecting the 3D microseismicevents in the subsets 610, 620, 630, and 640 of FIG. 6 onto a horizontalreference plane 850, respectively. Based on the four sets of 2Dmicroseismic data, the four boundaries 815, 825, 835, and 845 can beconstructed. The example boundaries 815, 825, 835, and 845 are 2D convexpolygons. Other types of two-dimensional boundaries can be computed. Thesizes of the polygons can represent the stimulated area contacting thesubterranean region. A 2D convex polygon can be calculated in a mannerthat is analogous to the process of constructing a 3D convex hull, or inanother manner. In some other implementations, the 2D boundaries may beobtained by projecting the constructed 3D boundaries 710, 720, 730, and740 onto the reference plane 850. In some implementations, the 2Dgeometrical representation of the stimulated contact area can be of adifferent shape and may be calculated using another technique.

In some instances, analysis and estimation of SRV can be performed inreal time, for example, during the collection of microseismic events.The example techniques described here can be applied, for example, to areal-time hydraulic fracturing process, for multi-stage completions withmultiple perforation clusters in a stage, or in other contexts.

In some cases, stimulated volumes can start and emit from perforationpoints on the wellbore. As such, at an initial phase of treatment, eachperforation cluster may be surrounded by a local region of stimulatedrock. As the hydraulic fracturing process evolves, the local regions ofstimulated rock can gradually grow. In some instances, several localregions or paths of stimulated rock can merge, and eventually form alarger volume of stimulated rock.

As an example aspect of operation, an algorithm for computing SRV inreal time includes obtaining input information related to theperforation clusters at each stage, for example, including the number ofperforations, location of each perforation, distance between twoadjacent perforations, or other information. At the initial time periodof the hydraulic fracturing treatment, as a new microseismic event isdetected, the distance from this event to each perforation can becalculated. The event can be associated with the perforation that hasthe minimum distance to the event and the event can be a supportingevent of the perforation.

In some implementations, the algorithm can start to generate an SRVrelated to a perforation when a minimum number of supporting events ofthe perforation have been accumulated. For instance, the minimum numberof supporting events can be four. With the four supporting events, atetrahedron can be constructed; the tetrahedron can represent theinitial local region of stimulated rock associated with the perforation.In some aspects of implementations, once a local region associated witha perforation is identified, the perforation can be defined as thecenter of the local region, or the center of the local region may bedefined otherwise.

When a new event appears on the buffer, it can be associated with thecenter or the perforation. In some instances, there may be three cases:a) a distance from the event to the center is larger than the distancefrom the center to its adjacent center; otherwise, the following twocases can be considered: b) the event lies outside the local region; c)the event lies within the local region. In case c), the new event doesnot affect the local region. In case b), the new event can make thelocal region propagate into its surroundings and grow. In someimplementations, the new event can become a vertex of an expandedboundary, for example, based on an example process described below. Incase a), the local region can be merged with its neighbor, for example,a local region or events associated with its adjacent perforation. In anext level, the algorithm can merge the events associated with twoadjacent centers or perforations and then use the set of merged eventsto construct a larger boundary (e.g., a convex hull, or another type ofboundary) to represent the stimulated rock region that contains themerged events. The center of the new boundary can be the average of theset of the two adjacent centers or perforations. In someimplementations, as long as new events are being detected, the recurrentprocess can be applied until the boundaries associated with theperforations are merged into a common boundary. In some implementations,during the accumulation of microseismic events, the algorithm can enableusers to visualize the temporal and spatial evolution of the stimulatedrock region and their merging processes.

In some implementations, the boundary can enclose all detectedmicroseismic events. The center of the boundary can be the average ofits vertices or another location. When a new event is detected, if theevent lies inside the local region, it does not affect the local region;otherwise, it can make the local region propagate into its surroundingsand grow into a larger region. In some instances, the latter situationcan include two cases.

The first case is that the new event is visible to only one facet of thelocal region. For example, as illustrated in FIG. 3A, the new event,e.g., event 306 a (assuming no events 306 b and 306 c) is visible onlyto the facet 320 a of the boundary 308 a. In other words, the new event306 a and the center of the boundary 308 a lie on opposite sides withrespect to the facet 320 a while they lie on the same side with respectto other facets. In this case, the facet 320 a can be deleted, and thealgorithm can use the new event 306 a along with any two vertices on thefacet 320 a to create three new triangular facets, for example, facets320 b, 320 c, and 320 d as plotted in FIG. 3B. As the new event 306 a isadded, the local region of stimulated rock dynamically propagates andgrows, for example, from the boundary 308 a to the updated boundary 308b.

The second case is that the new event is visible to multiple facets ofthe boundary. For example, as depicted in FIG. 4A, the new event, e.g.,event 406 a is visible to three facets 420 a, 420 b, and 420 c. In otherwords, the event 406 a and the center of the boundary 408 a lie onopposite sides with respect to the facets 420 a, 420 b, and 420 c whilethey lie on the same side with respect to other facets. In this case,the boundary 440 of these three facets can be identified and the threefacets 420 a, 420 b, and 420 c can be deleted. The new event 406 a andany two adjacent vertices on the identified boundary 440 can be used tocreate new facets, for example, facets 420 d-420 h as shown in FIG. 4B.As the new event 406 a is enclosed, the local region of stimulated rockdynamically propagates and grows, for example, from the boundary 408 ato the updated boundary 408 b.

In some instances, one challenge of real-time SRV analysis can beidentifying outliers as well as events with low density. Such events maynot be readily identifiable during the stimulation treatment. In someimplementations, outliers and events with low density can be identifiedand removed after the treatment, for example, following the sametechnique discussed with respect to FIG. 5A. Then the algorithm can usethe remaining microseismic events to refine the constructed boundary andobtain more accurate SRV. In some implementations, outliers and eventswith low density may be identified and removed in real time during thetreatment. As an example technique, a probability may be tagged with anew microseismic event. Outliers and events with low event density canbe identified, for example, by comparing a threshold with theprobability associated with the new event. Additional or differenttechniques can be used to identify the outliers and low density eventsin real time. The identified outlier and event with low density can beremoved in real time and the SRV can be dynamically estimated andanalyzed based on remaining events.

In some implementations, experience shows that the accuracy of the SRVestimation becomes more accurate as more microseismic events accumulate.In some instances, removing outliers and events with low density canhelp refine the geometrical object constructed based on the microseismicevents and improve the accuracy of SRV estimation. For instance,especially at early times of real-time SRV estimation, removing outliersand low density events can reduce or eliminate interference introducedby the outliers and low density events which are reflections ofactivities other than the considered injection treatment. In someinstances, the real-time SRV calculation algorithm can monotonicallyincrease the SRV estimation accuracy as the microseismic eventsaccumulate and can help maximize the SRV estimation accuracy.

In some instances, in addition to the volume, other geometric propertiesof a stimulated subterranean region can be estimated or otherwiseidentified based on microseismic events as well. The geometricproperties can include, for example, a length, width, height,orientation, or another attribute of the SRV for the stimulated region.In some instances, these geometric properties can provide a moreadequate and concrete description of the SRV and an overall fracturenetwork within the stimulated reservoir. In some instances, moreinformation of the stimulation region can be extracted based on thegeometric properties. Field engineers, operational engineers andanalysts, and others can better visualize, learn, or otherwise analyzethe subterranean region, and can manage the stimulation treatmentaccordingly.

In some implementations, the geometric properties of the SRV for thestimulated region can be identified based on a computed SRV boundary.For instance, a major axis of the SRV can be identified based on the SRVboundary. The major axis can include information regarding, for example,lateral extension and orientation as well as the development of thestimulated region. For example, the major axis may reflect the extensionand orientation of the primary fractures of the fracture network insidethe stimulated region. Additional or different geometric properties andinformation can be identified based on the SRV boundary.

The SRV boundary can include, for example, a sphere, a cube, anellipsoid, a cylinder, a polyhedron, or another geometrical object. As aspecific example, the SRV boundary can include an ellipsoid. Thegeometric properties of the ellipsoid can be used to quantify andcharacterize the geometric properties of the stimulated region and thefracture network inside the stimulated region. For instance, anellipsoid in a Cartesian coordinate system can be characterized by nineparameters that include, a center, semi-lengths of x-axis, y-axis andz-axis, and rotation angles along these axes. In some implementations,the lengths of semi-axes can be used to approximate or otherwiserepresent the length, width and height of the SRV for the stimulatedregion and the rotation angles can be used to characterize theorientation of the SRV for the stimulated region. In someimplementations, additional or different parameters can be selected todescribe the geometric properties of the stimulated region.

Various algorithms and methods can be used to construct an ellipsoidbased on the microseismic event locations associated with a stimulationtreatment. One example approach can involve fitting an ellipsoid to aset of microseismic event locations. As a specific example, the set oflocations can include the vertices of a computed SRV boundary (e.g., aconvex hull). The ellipsoid can be computed according to a least squaremethod such that the distances between the ellipsoid and the vertices ofthe convex hull are minimized. The ellipsoid can be computed based onadditional or different principles or techniques.

FIG. 15A is a plot 1500 a showing an example of a boundary 1508 and itsvertices 1516; FIG. 15B is a plot 1500 b showing an ellipsoid 1509associated with the example boundary 1508 in FIG. 15A. In theillustrated example, the boundary 1508 is a convex hull constructedbased on the microseismic events 1506 shown in FIG. 15B. The boundary1508 can be computed according to the example operations described withrespect to FIGS. 2A-5B, or in another manner. In some implementations,suppose the boundary 1508 has n vertices 1516, the location of eachvertex may be denoted as (x_(i), y_(i), z_(i)), 1≦i≦n. In Cartesiancoordinates, a general ellipsoid may be described as in equation (11)a ₁ x ² +a ₂ y ² +a ₃ z ²+2a ₄ xy+2a ₅ xz+2a ₆ yz+2a ₇ x+2a ₈ y+2a ₉ z+a₁₀=0  (11)with coefficients a₁˜a₁₀. The ten coefficients can be subject to theconstraints: a₄<a₁ a₂, a₅<a₁ a₃, a₆<a₂ a₃. In some implementations, toreduce the complexity, additional constraints can be applied on one ormore of these parameters. For example, it can be assumed that the originof the ellipsoid is not on the ellipsoid surface, for instance, a₁₀≠0and equation (11) may be normalized and described as in equation (12)with nine parameters a₁˜a₉:a ₁ x ² +a ₂ y ² +a ₃ z ²+2a ₄ xy+2a ₅ xz+2a ₆ yz+2a ₇ x+2a ₈ y+2a ₉z=1  (12).

In some instances, the condition for fitting the ellipsoid described byequation (12) using n points (vertices) can be n≧9. Defining two vectorsa, x asa=[a₁a₂a₃a₄a₅a₆a₇a₈a₉]^(T),  (13-a)x=[x²y²z²2xy2xz2yz2x2y2z]^(T)  (13-b),equation (12) can have a simplified form of a dot product: a·x=1, wherethe superscript T is the transpose operation on vectors or matrices. Then points (e.g., the vertices on the boundary) can define a n×9 matrix D,

$\begin{matrix}{D = {\begin{bmatrix}x_{1}^{2} & y_{1}^{2} & z_{1}^{2} & {2x_{1}y_{1}} & {2x_{1}z_{1}} & {2y_{1}z_{1}} & {2x_{1}} & {2y_{1}} & {2z_{1}} \\x_{2}^{2} & y_{2}^{2} & z_{2}^{2} & {2x_{2}y_{2}} & {2x_{2}z_{2}} & {2y_{2}z_{2}} & {2x_{2}} & {2y_{2}} & {2z_{2}} \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\x_{n}^{2} & y_{n}^{2} & z_{n}^{2} & {2x_{n}y_{n}} & {2x_{n}z_{n}} & {2y_{n}z_{n}} & {2x_{n}} & {2y_{n}} & {2z_{n}}\end{bmatrix}_{n \times 9}.}} & (14)\end{matrix}$

As an example, parameters a of an ellipsoid that best fits the n pointsin a least square sense can be calculated, for example, by solving alinear system (15):D^(T)Da=D^(T)b,  (15-a)b=[1 1 . . . 1 1]^(T) _(n×1)  (15-b).

In some instances, it can be shown that a unique solution exists forthis linear system (15). In some implementations, the linear system (15)can be solved analytically, for example, via an analytic (or direct)approach, or numerically, for example, via the Gaussian elimination orGauss Jordan elimination method. Additional or different approaches canbe used. In some instances, the analytic or direct approach can be timeconsuming and computationally complex.

In some implementations, the ellipsoid represented by the equation (12)can also be represented in a standard form:

$\begin{matrix}{{\frac{x^{\prime 2}}{a^{2}} + \frac{y^{\prime 2}}{b^{2}} + \frac{z^{\prime 2}}{c^{2}}} = 1} & (16)\end{matrix}$by definingx′=a cos u sin v,  (17-a)y′=b sin u cos v,  (17-b)z′=c cos v,  (17-c)uε[0,360°),  (17-d)vε[0,180°)  (17-e),and using the following linear transformations (18):

$\begin{matrix}{{\begin{bmatrix}x \\y \\z\end{bmatrix} = {{R_{z}R_{y}{R_{x}\begin{bmatrix}x^{\prime} \\y^{\prime} \\z^{\prime}\end{bmatrix}}} + \begin{bmatrix}x_{0} \\y_{0} \\z_{0}\end{bmatrix}}},} & \left( {18\text{-}a} \right) \\{{R_{x} = \begin{bmatrix}1 & 0 & 0 \\0 & {\cos\;\theta_{x}} & {{- \sin}\;\theta_{x}} \\0 & {\sin\;\theta_{x}} & {\cos\;\theta_{x}}\end{bmatrix}},} & \left( {18\text{-}b} \right) \\{{R_{y} = \begin{bmatrix}{\cos\;\theta_{y}} & 0 & {\sin\;\theta_{y}} \\0 & 1 & 0 \\{{- \sin}\;\theta_{y}} & 0 & {\cos\;\theta_{y}}\end{bmatrix}},} & \left( {18\text{-}c} \right) \\{R_{z} = {\begin{bmatrix}{\cos\;\theta_{z}} & {{- \sin}\;\theta_{z}} & 0 \\{\sin\;\theta_{z}} & {\cos\;\theta_{z}} & 0 \\0 & 0 & 1\end{bmatrix}.}} & \left( {18\text{-}d} \right)\end{matrix}$

Here a, b, c are lengths of semi-axes, θ_(x), θ_(y), θ_(z) are rotationangles around the x-axis, y-axis and z-axis, R_(x), R_(y), R_(z) arerotation operations, and (x₀, y₀, z₀) is the center of the ellipsoid. Insome instances, the positive value of the rotation angle can representthe counterclockwise direction; the negative value can represent theclockwise direction. The following nine parametersa,b,c,θ_(x),θ_(y),θ_(z),x₀,y₀,z₀  (19)can be function parameters that can have geometrical and physicalinterpretations for describing the ellipsoid's properties andcharacterizing the geometry of the stimulated region. The values for thenine parameters can be derived based on equation (12). For example, thenine parameters in equation (12) can be presented in the form of asymmetric 4×4 matrix A

$\begin{matrix}{{A = \begin{bmatrix}a_{1} & a_{4} & a_{5} & a_{7} \\a_{4} & a_{2} & a_{6} & a_{8} \\a_{8} & a_{6} & a_{3} & a_{9} \\a_{7} & a_{8} & a_{9} & {- 1}\end{bmatrix}},} & \left( {20\text{-}a} \right)\end{matrix}$and the equation (12) can be rewritten in a matrix form asX^(T)AX=0,  (20-b)where

$\begin{matrix}{X = {\begin{bmatrix}x \\y \\z \\1\end{bmatrix}.}} & \left( {20\text{-}c} \right)\end{matrix}$

The center of the ellipsoid (x₀, y₀, z₀) can be calculated by equation(21):

$\begin{matrix}{\begin{bmatrix}x_{0} \\y_{0} \\z_{0}\end{bmatrix} = {- {{\begin{bmatrix}a_{1} & a_{4} & a_{5} \\a_{4} & a_{2} & a_{6} \\a_{5} & a_{6} & a_{3}\end{bmatrix}^{- 1}\begin{bmatrix}a_{7} \\a_{8} \\a_{9}\end{bmatrix}}.}}} & (21)\end{matrix}$

The translation operation of the ellipsoid by the quantities {circumflexover (x)}=x−x₀, ŷ=y−y₀, {circumflex over (z)}=z−z₀ can be given bytranslation matrix T,

$\begin{matrix}{{T = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\x_{0} & y_{0} & z_{0} & 1\end{bmatrix}},} & (22)\end{matrix}$which can transform the matrix A into another matrix A′ by

$\begin{matrix}{A^{\prime} = {{TAT}^{T} = \begin{bmatrix}a_{1} & a_{4} & a_{5} & 0 \\a_{4} & a_{2} & a_{6} & 0 \\a_{5} & a_{6} & a_{3} & 0 \\0 & 0 & 0 & {{a_{7}x_{0}} + {a_{8}y_{0}} + {a_{9}z_{0}} - 1}\end{bmatrix}}} & (23)\end{matrix}$

For notation simplification, x, y, z will be used instead of {circumflexover (x)}, ŷ, {circumflex over (z)} in the following. For example,defining

$\begin{matrix}{{\alpha = {{{- a_{5}}x_{0}} - {a_{6}y_{0}} - {a_{7}z_{0}} + 1}},} & \left( {24\text{-}a} \right) \\{{b_{1} = \frac{a_{1}}{\alpha}},} & \left( {24\text{-}b} \right) \\{{b_{2} = \frac{a_{2}}{\alpha}},} & \left( {24\text{-}c} \right) \\{{b_{3} = \frac{a_{3}}{\alpha}},} & \left( {24\text{-}d} \right) \\{{b_{4} = \frac{a_{4}}{\alpha}},} & \left( {24\text{-}e} \right) \\{{b_{5} = \frac{a_{5}}{\alpha}},} & \left( {24\text{-}f} \right) \\{b_{6} = {\frac{a_{6}}{\alpha}.}} & \left( {24\text{-}g} \right)\end{matrix}$then the ellipsoid equation (12) with the center (0,0,0) can becomeb ₁ x ² +b ₂ y ² +b ₃ z ²+2b ₄ xy+2b ₅ xz+2b ₆ yz=1  (25)and it can also be structured using a symmetric 3×3 matrix B

$\begin{matrix}{{{Y^{T}{BY}} = 1},} & \left( {26\text{-}a} \right) \\{{B = \begin{bmatrix}b_{1} & b_{4} & b_{5} \\b_{4} & b_{2} & b_{6} \\b_{5} & b_{6} & b_{3}\end{bmatrix}},} & \left( {26\text{-}b} \right) \\{Y = {\begin{bmatrix}x \\y \\z\end{bmatrix}.}} & \left( {26\text{-}c} \right)\end{matrix}$

The three positive eigenvalues λ₁, μ₂, μ₃ of the 3×3 symmetric matrix Bcan be solved by analytic method but may have a complicated analyticsolution. In some implementations, another approach can be used. Forinstance, the lengths of semi-axes can be calculated by

$\begin{matrix}{{a = \frac{1}{\sqrt{\lambda_{1}}}},} & \left( {27\text{-}a} \right) \\{{b = \frac{1}{\sqrt{\lambda_{2}}}},} & \left( {27\text{-}b} \right) \\{c = {\frac{1}{\sqrt{\lambda_{3}}}.}} & \left( {27\text{-}c} \right)\end{matrix}$

The unit eigenvector P_(i) for the eigenvalue λ_(i), 1≦i≦3, can beobtained, for example, by using the “power” numerical algorithm, oranother technique. Three resulting eigenvectors can construct anorthonormal matrix P=[P₁ P₂ P₃]=[p_(ij)] as follows:

$\begin{matrix}{{{P^{T}P} = I_{3 \times 3}},} & \left( {29\text{-}a} \right) \\{{{P^{T}{BP}} = \begin{bmatrix}\lambda_{1} & 0 & 0 \\0 & \lambda_{2} & 0 \\0 & 0 & \lambda_{3}\end{bmatrix}},} & \left( {29\text{-}b} \right) \\{P = {R_{z}R_{y}{R_{x}.}}} & \left( {29\text{-}c} \right)\end{matrix}$

Three rotation angles can be given by

$\begin{matrix}{{\theta_{x} = {\tan^{- 1}\frac{p_{32}}{p_{33}}}},} & \left( {30\text{-}a} \right) \\{{\theta_{y} = {- {\sin^{- 1}\left( p_{31} \right)}}},} & \left( {30\text{-}b} \right) \\{\theta_{z} = {\tan^{- 1}\frac{p_{21}}{p_{11}}}} & \left( {30\text{-}c} \right)\end{matrix}$where p_(ij) are items of the matrix P.

The example process for calculating the functional parameters (e.g., theparameters listed in formula (19)) and identifying geometric propertiesof the ellipsoid can start by generating the matrix D according toequation (14), for example, by using all vertices of an SRV boundary(e.g., the convex hull 1508 in FIG. 15A). Then, solving equation (15)for vector a can yield the nine parameters a₁˜a₉ of the ellipsoidequation (12). Based on the equation (12), the center, lengths ofsemi-axes, and rotation angles of the ellipsoid can be obtained, forexample, using equation (21), equation (27) and equation (30),respectively. Additional or different techniques can be used forderiving the parameters of the ellipsoid.

In some instances, the rotation angles along the x-axis and y-axis(θ_(x), θ_(y)) can be much smaller than the rotation angle along z-axis(θ_(z)). In some instances, for example, referring to the standardellipsoid representation (16), out of the nine parameters in (19), fourparameters of the ellipsoid may play a more important role in describingthe property of the stimulated region: the length of stimulated rock,which may be quantified by the larger between 2a and 2b, the width ofthe stimulated rock, which may be approximated by the smaller between 2aand 2b, the height, which may be described by a value of 2c, and therotation angle along z-axis (θ_(z)), implicating the stimulated region'sazimuth, which can be either θ_(z) or 90°−θ_(z). In someimplementations, the orientation azimuth identified based on the SRVboundary can be compared, for example, with the fracture pattern azimuthidentified by fracture matching technology or another technique.Additional or different parameters can be selected to characterize theSRV for the stimulated region.

In the illustrated example in FIG. 15B, the ellipsoid 1509 correspondingto the boundary 1508 in FIG. 15A has a center at (−1030.68, 2145.09,7973.13) (feet). Its lengths of semi-axes a, b, and c are 866.43, 384.40and 241.23 (feet), and the rotation angles are 2.14°, 1.6° and 50.1°,respectively. The top of the ellipsoid 1509 can be removed so that themicroseismic events 1506 inside the ellipsoid 1509 and the wellbore 1550and perforation clusters 1560 can be illustrated and examined. Thelength, width and height of the stimulated region are 1732.86, 768.8 and482.46 (feet) according to the algorithm described above. The azimuth ofthe stimulated region is 90.0°−50.1°=39.9° north-to-east. In someinstances, the length of the stimulated region can represent theextension of the hydraulic fracture network to the reservoir while thewidth can relate to the number of fractures in the primary fracturefamily. The azimuth of the stimulated region can represent theorientation of the primary fracture family in the subterranean region.

In some implementations, the approximated ellipsoid can be viewed as acontainer of microseismic events and hydraulic fractures in thestimulated region. The ellipsoid can be the boundary that contactsbetween the stimulated reservoir and the un-fractured reservoir. In someinstances, it is very useful to provide the well operators and fieldengineers with visualization of hydraulic fractures, development of thehydraulic fractures, as well as the SRV boundary that captures the shapeof the stimulated region and encloses the microseismic activities andthe hydraulic fractures.

FIG. 16A is a plot showing a view of an example visualization 1600 a ofmicroseismic events, hydraulic fractures, and the SRV boundary. Inaddition to the microseismic events 1506 and the approximated ellipsoid1509 shown in FIG. 15B, the example visualization 1600 a includes ninehydraulic fractures 1616 identified based on the microseismic events1506. The hydraulic fractures 1616 can be identified, for example, byfracture matching technology, such as Halliburton's “Foray 3DMicroseismic Fracture Matching Services,” or other techniques may beused. In some implementations, a real-time development of the hydraulicfractures 1616 can be identified, tracked, and visually presented, forexample, by Halliburton's “Foray 3D Real Time Microseismic FractureMatching Services,” or other techniques may be used. In someimplementations, the characteristics of these hydraulic fractures 1616can be described by the average values of the nine fractures 1616, forexample, average azimuth 35.1°, average dip angle 76.1°, averagehalf-length 627 (feet), average height 338 (feet), and average spacing72.2 (feet). The fracture length, fracture spacing, and fracture heightof the fracture network (e.g., characterized by the identified hydraulicfractures 1616) have a close correlation with the length, width andheight of the stimulated region (e.g., characterized by the ellipsoid1509). In the illustrated example, the average azimuth (N35.1° E) offractures 1616 is consistent with the azimuth (N39.9° E) of theellipsoid 1509 for the stimulated region, which confirms the correctnessof the techniques described herein.

FIG. 16B is a plot showing another view 1600 b of the examplevisualization 1600 a in FIG. 16A. The view 1600 b in FIG. 16B providesanother perspective of the extension, spacing, and orientation of theidentified fractures 1616 as well as the shape and orientation of theellipsoid 1509, for example, relative to the wellbore 1550 and theperforation clusters 1560. In some implementations, view, perspective,size, or another display functionality of the visualization 1600 a canbe adjusted or otherwise controlled by a user (e.g., a well operator, afield engineer, an analyst, etc.) to facilitate their view and analysis.For example, the user may select, zoom in and out, rotate, or otherwisemanage a portion of the entire visualization, for example, for closeexamination. In some implementations, when a specific portion (e.g., oneof the identified fracture plane 1616 or the ellipsoid 1509) isselected, its attributes or parameters (e.g., azimuth, dip angle,half-length, height, and spacing or density size, extension, length,width, height, orientation, area, volume, etc.) can be displayed orotherwise output. Additional or different actions can be applied.

In some instances, the microseismic events, the fractures, and the SRVboundary can be computed and displayed in real time based onmicroseismic data. In some implementations, the development of thehydraulic fractures and the SRV can be approximated and tracked. In someinstances, the user can visualize, for example, the propagation orgrowth direction, the width, the shape, or another attribute of thehydraulic fractures and the SRV. The graphic realization of theidentified SRV boundary and hydraulic fractures can provide the user adirect and intuitive tool to understand the subterranean region, andevaluate, control, design, or otherwise manage the stimulationtreatment. For instance, through the visualization, whether thefractures intersect or will intersect the wellbore 1550 at unexpectedpoints or whether the fractures divert from their expected direction canbe determined. In these cases, preventive actions can be taken tocontrol the developments of the fracture network and the stimulatedregion. Additional or different information can be observed or otherwiseextracted based on the visualization.

FIG. 17 is a plot 1700 showing example SRV boundaries calculated fromexample microseismic event data collected from a multi-stage injectiontreatment. The example plot 1700 shows four subsets of microseismicevents: 1710 (shown as circles), 1720 (shown as squares), 1730 (shown astriangles), and 1740 (shown as diamonds) associated with stage 1, stage2, stage 3, and stage 4 of the example four-stage injection treatment,respectively. Four SRV boundaries 1715, 1725, 1735, and 1745 arecomputed based on the four subsets 1710, 1720, 1730, and 1740 of themicroseismic events, respectively. Each of the four ellipsoids 1715,1725, 1735, and 1745 can be computed based on the example techniquedescribed with respect to FIGS. 15A-B, or in another manner. The tops ofthe illustrated ellipsoids 1715, 1725, 1735, and 1745 are removed toshow the subsets of microseismic events 1710, 1720, 1730, and 1740. Theellipsoids 1715, 1725, 1735, and 1745 provide a respective 3Dvisualization of the geophysical shape of the SRV for each treatmentstage. The size and orientation of the stimulated region for each stage,as well as SRV overlaps between stages, can be identified based on thecomputed ellipsoids 1715, 1725, 1735, and 1745 and their visualizations.

FIG. 9 is a flow chart showing an example process 900 for processingmicroseismic data. All or part of the example process 900 may becomputer-implemented, for example, using the features and attributes ofthe example computing subsystem 110 shown in FIG. 1B or other computingsystems. The process 900, individual operations of the process 900, orgroups of operations may be iterated or performed simultaneously toachieve a desired result. In some cases, the process 900 may include thesame, additional, fewer, or different operations performed in the sameor a different order. The process 900 may be performed on site near awellbore, at a remote location, or in another location.

At 910, a stimulation treatment is performed. The stimulation treatmentcan be a single-stage injection treatment or a multi-stage injectiontreatment. The injection treatment may be performed, for example, by thewell system 100 in FIG. 1A or by another type of system. The injectiontreatment can induce and generate microseismic events in the stimulatedsubterranean region.

At 920, microseismic data can be collected. The microseismic data can becollected, for example, by sensors (e.g., sensors 136 in FIG. 1A) ordata collection apparatus of an injection treatment system. Themicroseismic data can be collected before, during, or after astimulation treatment or at another time. In some implementations, themicroseismic event data can be collected in real time (or substantiallyin real time) during a stimulation treatment. For example, themicroseismic data may be collected at individual stages of a multi-stageinjection treatment. The microseismic data can include any suitableinformation of microseismic events associated with a stimulationtreatment of a subterranean region. In some aspects of implementations,the microseismic data can be stored in a memory (e.g., memory 150) of acomputing system for storage or further processing.

In some instances, microseismic events may have low-amplitude orlow-energy (e.g., with the value of the log of the intensity or momentmagnitude of less than three), or a low signal-to-noise ratio (SNR).Some uncertainty, inaccuracy, or measurement error can be associatedwith the event locations. For example, the uncertainty can include alocation uncertainty, a moment (e.g., amplitude or energy) uncertainty,a time uncertainty (e.g., the uncertainty related to associating anevent with a particular treatment stage), or a combination of these andother types of uncertainty. In some implementations, the uncertainty ofa microseismic event can be approximated, for example, by a ball withradius r given by equation (2), or can be described in another manner.For instance, the uncertainty may be described by a prolate spheroid oranother geometrical representation, which has the highest likelihood atthe center and the lowest likelihood at the edge of the geometricalrepresentation.

At 930, microseismic data can be filtered. The microseismic data can befiltered based on times, locations, uncertainties, magnitude, moment,energy, event density, or a combination of these and other attributes ofthe microseismic events. In some implementations, the microseismic datacan include microseismic events associated with multiple stages of astimulation treatment. The microseismic data can be filtered, forexample, by grouping microseismic events associated with respectivestages of the multi-stage injection treatment. In some aspects, themicroseismic data associated with the entire multi-stage injectiontreatment can form a superset of microseismic events; the microseismicevents associated with each stage can form a respective subset. In someimplementations, the microseismic data can be filtered by removingoutliers from a subset, a superset, or another set of microseismicevents. In some instances, the outliers can include deterministicoutliers, statistical outliers, or another type of outliers. Theoutliers can include one or more microseismic events with locationsoutside a range, with uncertainty beyond a threshold, with amplitude,energy, or event density below a threshold, or with other outlierattributes. The outliers can be filtered by removing the microseismicevents exceeding an attribute threshold, beyond certain statisticaldeviation, etc.; or outliers can be filtered in another manner. In someimplementations, the attribute threshold (e.g., density threshold,distance threshold, moment threshold, etc.) can be a user input controlparameter or it can be configured automatically, for example, by dataprocessing apparatus, based on system setup, reservoir property,treatment plan, or a combination of these and other parameters.

At 940, microseismic data can be analyzed. In some implementations, theanalysis can be performed based on the filtered microseismic data. Insome implementations, analyzing the microseismic data can includeidentifying stimulated reservoir geometry, calculating an SRV for astimulation treatment, identifying uncertainty of an SRV, fracturemapping and matching, or another type of processing. As an example,analyzing the microseismic data includes constructing a boundary ofmicroseismic events and calculating an SRV based on the boundary. Insome instances, uncertainty can be associated with the microseismicevents. In this case, uncertainty associated with the SRV calculationcan be identified based on the uncertainty of the microseismic events.Some example microseismic data analysis techniques are described withrespect to FIGS. 2A-8 and FIGS. 10-12. Analyzing the microseismic datacan include additional or different techniques.

In some implementations, filtering and analyzing the microseismic datacan be an iterative process with a terminating condition. For example,after analyzing the microseismic data at 940, the process 900 may goback to 930 for further microseismic data filtering. In some instances,the filtering can be based on the analyzed result at 940. For instance,the microseismic events may be filtered by removing low event densityevents that are vertices of a constructed boundary at 940. Themicroseismic data can be filtered based on additional or differentcriteria. The filtered microseismic data can be analyzed at 940 again,for example, for constructing an improved boundary. In someimplementations, filtering and analyzing the microseismic data can berepeated until, for example, a predefined number of iterations isreached, outliers and low density events have been filtered, or anotherterminating condition is reached. In some implementations, themicroseismic data can be filtered and analyzed in real time (orsubstantially in real time) during a stimulation treatment, or atanother suitable time. In some implementations, the analyzing process at940 can include the filtering process at 930.

At 950, the analyzed result can be displayed. For instance, the analyzedresult can be displayed on a screen or another type of displayapparatus. In some implementations, the analyzed result can bedisplayed, for example, in real time (or substantially real time) as themicroseismic data are analyzed, after a final result is obtained, or atanother time (e.g., when requested by a user). The analyzed result caninclude, for example, a geometrical representation of SRV, extensions ofhydraulic fractures, or a combination of these and other types ofvisualizations. In some instances, the analyzed result can include aquantity of calculated SRV, uncertainty or accuracy of an SRV, anoverlapping volume of SRVs, a percentage of the overlapping volume overthe SRV of a treatment stage or of an entire injection treatment, orother information. FIGS. 2A-8 show example displays of analyzed results.Based on the displayed result, efficiency of a stimulation treatment canbe evaluated. In some instances, a current or a prospective injectionplan (e.g., injection schedules of future treatment stages, parametersof injection treatment, diversion techniques, etc.) can be adjustedbased on the result.

FIG. 10 is a flow chart showing an example process 1000 for identifyingan SRV from microseismic data. All or part of the example process 1000may be computer-implemented, for example, using the features andattributes of the example computing subsystem 110 shown in FIG. 1B orother computing systems. The process 1000, individual operations of theprocess 1000, or groups of operations may be iterated or performedsimultaneously to achieve a desired result. In some cases, the process1000 may include the same, additional, fewer, or different operationsperformed in the same or a different order.

At 1010, a subset of microseismic events can be selected. In someimplementations, the subset can be selected according to the filteringoperation at 930 in FIG. 9, or in another manner. For instance, thesubset of microseismic events can be selected from a superset ofmicroseismic events based on respective locations of the subset ofmicroseismic events. In some instances, the subset can includemicroseismic events whose locations are outliers in the superset ofmicroseismic events. Additionally or differently, the subset ofmicroseismic events can be selected based on respective event densitiesof the subset of microseismic events. For example, the subset caninclude microseismic events having event densities below a thresholddensity. The subset can be selected based on other criteria and mayinclude other microseismic events.

At 1020, a boundary can be calculated to enclose the locations of atleast a portion of the microseismic events not included in the selectedsubset at 1010. In some instances, the boundary is calculated to encloselocations of a second subset of microseismic events. The second subsetof microseismic events can be different than the selected subset ofmicroseismic events at 1010. As a specific example, the second subsetmay include remaining microseismic events after removing outliers, lowdensity events, or both in the selected subset at 1010. In someimplementations, the second subset can be selected from a superset ofmicroseismic events based on respective times of the second subset ofmicroseismic events. For instance, the second subset can includemicroseismic events that are associated with a single stage of amulti-stage injection treatment and the superset can include themicroseismic events associated with multiple stages (e.g., all stages,or fewer than all stages) of the multi-stage injection treatment. Insome instances, the second subset can be selected based on othercriteria and may include other microseismic events. In someimplementations, a subset hierarchy can be defined and the microseismicevents can be selected in a successive manner. As a specific example, afull set can include locations of all microseismic events collected fora multi-stage injection treatment. Multiple first-layer subsets may bedefined and selected such that they include locations of microseismicevents associated with an individual stage of the multi-stage injectiontreatment. One or more second-layer subsets of locations can be selectedfrom each of the first-layer subsets, for example, based on theirrespective locations, event densities, or any other attributes relativeto the first-layer subset. In this case, the first-layer subset can beregarded as a superset of the one or more second-layer subsets.Additional or different layered subsets can be defined and selected.

In some implementations, the boundary can be a geometricalrepresentation of a stimulated subterranean region and the volume of thegeometrical object enclosed by the boundary can be the SRV for thestimulation treatment applied on the subterranean region. In someinstances, the boundary can be a closed boundary. For example, theboundary can either intersect or contain each microseismic event in thesecond subset while the microseismic events in the selected subset at1010 reside outside the boundary. In some instances, a boundary can bedefined by discrete points (e.g., discrete microseismic events) or theboundary can include one or more edges, curves, facets, or a combinationof these and other geometrical elements. The boundary can be of anyappropriate shape, for example, a rectangle, a circle, a polygon, asphere, an ellipsoid, a polyhedron, etc. The boundary can be convex,concave, or have other geometric properties. In some implementations,the boundary can have two dimensions, three dimensions, etc. As anexample, the boundary can be a 3D convex hull (e.g., boundaries 208, 308a, 308 b, 408 a, 408 b, or 508), 2D convex polygon (e.g., convex polygon815, 825, 835, or 835), or an ellipsoid enclosing a set of microseismicevent locations. In some implementations, a boundary may be representedby certain parameters (e.g., a center, a radius, an angle, a curvature,the number of vertices, the number of edges, etc.). The boundary can becalculated by identifying the parameters that describe the boundary.

In some implementations, the boundary can be calculated by iterativelyidentifying triangular facets having vertices at respective groups ofthe microseismic event locations. For example, the boundary can becalculated according to the example operations described with respect toFIGS. 2A-5B. The example operations include, for example, identifyinginitial vertices and calculating an initial boundary. The initialvertices can be the microseismic events at extreme locations, or otherlocations. After calculating the initial boundary, an expansionoperation may be performed to expand the calculated boundary to encloseone or more microseismic events residing outside the initial boundary.The expansion operation may be repeated until a final boundary iscalculated. The final boundary can intersect or contain all microseismicevent locations in the second subset, or the final boundary can beconfigured to satisfy other criteria. In some implementations,microseismic events with low event density can be removed from thesecond subset. For example, a vertex of a calculated boundary with anevent density below a threshold density can be removed. A refinedboundary can be calculated based on the remaining microseismic events.In some implementations, the boundary can be calculated based onadditional or different techniques.

In some implementations, a 2D boundary can be calculated, for example,according to a similar process described above, based on the exampletechnique described with respect to FIG. 8, or based on additional ordifferent techniques. For instance, calculating a 2D boundary mayinvolve projecting 3D microseismic events onto a reference plane (e.g.,the horizontal plane), for example, as given by equations (8)-(10) andcomputing the 2D boundary based on the projected 2D events.

At 1030, an SRV can be estimated or otherwise identified based on thecalculated boundary. For example, the SRV can be identified bycalculating the interior volume of the boundary. An example techniquefor calculating the volume of the boundary is described with respect toFIG. 5A, for example, by identifying a center of the boundary;constructing a tetrahedron whose one vertex is the center and otherthree vertices are the three vertices of each facet of the boundary;calculating and summing up the volumes of each constructed tetrahedron.In some implementations, additional or different techniques may be usedto calculate the quantity of SRV. For example, the calculated boundarymay be represented by parameters (e.g., a center, a radius, an angle, acurvature, the number of vertices, the number of edges, etc.), and theSRV can be identified by calculating a volume of the boundary, forexample, based on the parameters of the boundary, a volume computation,or other considerations.

At 1040, the boundary can be displayed. In some implementations, theboundary can be displayed in the manner described with respect to 950 inFIG. 9. For instance, the boundary can be displayed as a geometricobject (e.g., a convex hull, or another type of object) as shown inFIGS. 2A-5B. The calculated quantity of SRV can be displayed as well. Insome instances, the boundary, the SRV quantity, or other SRV data can bedisplayed in real time during a stimulation treatment.

FIG. 11 is a flow chart showing an example process 1100 for identifyinguncertainty associated with a stimulated reservoir volume (SRV)calculation. All or part of the example process 1100 may becomputer-implemented, for example, using the features and attributes ofthe example computing subsystem 110 shown in FIG. 1B or other computingsystems. The process 1100, individual operations of the process 1100, orgroups of operations may be iterated or performed simultaneously toachieve a desired result. In some cases, the process 1100 may includethe same, additional, fewer, or different operations performed in thesame or a different order.

At 1110, an SRV boundary can be computed based on microseismic eventlocations. In some implementations, the microseismic events areassociated with a single stage of a multi-stage injection treatment. TheSRV boundary can be used to identify the SRV for the single-stage of aninjection treatment. The SRV boundary can be computed according to oneor more operations of the example process 1000, or in another manner. Insome instances, the SRV boundary may include multiple vertices andfacets. For example, the boundary 508 shown in FIG. 5A can be an exampleSRV boundary.

At 1120, an inner boundary can be computed. The inner boundary and theSRV boundary can be defined in a common spatial domain. The commonspatial domain, for example, can be a 3D or 2D coordinate system (e.g.,spherical coordinates, rectangular coordinates, etc.) or another domain.In some implementations, the inner boundary can be calculated based onuncertainties (e.g., azimuth uncertainty, distance uncertainty and depthuncertainty, moment uncertainty, time uncertainty, etc.) of themicroseismic events in the common domain. For example, the innerboundary can be calculated based on respective interior points ofvertices of the SRV boundary as described with respect to FIG. 5B. Theinterior points of the vertices can reside inside the SRV boundary withrespective distances. In some instances, the respective distances candepend on the location uncertainties of the microseismic events at thevertices. For example, the respective distances may be r determined bythe equation (2), or the distances can be determined in another manner.In some instances, an interior point of a vertex of the SRV boundary canlie on a segment connecting the vertex and the center of the SRVboundary. In this case, the coordinate components of the interior pointcan be given by equations (3-a), (3-b), and (3-c), or the interior pointcan reside in another location inside the SRV boundary. Afteridentifying the interior points of the vertices of the SRV boundary, theinner boundary can be calculated, for example, by connecting theinterior points, by following one or more operations of the exampleprocess 1000 based on the interior points, or by using anothertechnique. The boundary 507 in FIG. 5B can be an example inner boundaryassociated with the example SRV boundary 508 in FIG. 5A, both defined ina common spatial domain with axes 504 a-c.

At 1130, an outer boundary can be computed. The outer boundary and theinner boundary can be defined in the common domain. At least a portionof the outer boundary can reside outside the inner boundary. In someinstances, the inner boundary resides wholly within the outer boundary.The outer boundary can be calculated based on location uncertainties ofthe microseismic events in the common domain. For example, the outerboundary can be calculated based on respective exterior points ofvertices of the SRV boundary as described with respect to FIG. 5B. Theexterior points of the vertices can reside outside the SRV boundary withrespective distances. The respective distances can depend on thelocation uncertainties of the microseismic events at the vertices. Forinstance, the respective distance may be r determined by the equation(2), or the distance can be determined in another manner. In someinstances, an exterior point of a vertex of the SRV boundary can lie ona ray starting from the center of the SRV and extending through thevertex. In this case, the coordinate components of the exterior pointcan be given by equations (4-a), (4-b), and (4-c), or the exterior pointcan reside in another location outside the SRV boundary. Afteridentifying exterior points of the vertices of the SRV boundary, theouter boundary can be computed, for example, by connecting the exteriorpoints, by following one or more operations of the example process 1000based on the exterior points, or by using another suitable technique.The boundary 509 in FIG. 5B can be an example outer boundary associatedwith the example SRV boundary 508 in FIG. 5A, both defined in the commonspatial domain with axes 504 a-c.

In some implementations, the SRV boundary, the inner boundary, or theouter boundary can be of any suitable dimension, for example, based onthe spatial domain that they reside in. For example, in some instances,the common spatial domain of the SRV boundary, the inner boundary, andthe outer boundary can include a three-dimensional space, and the threeboundaries can be three-dimensional boundaries (e.g., as shown in FIGS.5A-B). In some other instances, the common domain can include atwo-dimensional space, and the three boundaries can be two-dimensionalboundaries.

At 1140, an uncertainty of the SRV can be identified based on the innerand outer boundaries. In some instances, the uncertainty of the SRV canbe identified as a difference in volume between the inner and outerboundaries. For example, an uncertainty of the SRV associated with theboundary 508 can be the difference in volume between the inner boundary507 and the outer boundary 509 as shown and described with respect toFIG. 5B. The uncertainty of SRV may be calculated based on additional ordifferent measurement. In some implementations, additional or differentdata can be calculated. For example, the percentage of the uncertaintyof the SRV over the SRV quantity can be calculated and serve as anaccuracy measurement or a confidence level associated with the SRVcalculation.

At 1150, one or more of the SRV boundary, the inner boundary, or theouter boundary can be displayed. In some implementations, one of theboundaries can be displayed in the manner described with respect to 950in FIG. 9. For instance, one or more of the boundaries can be displayedas geometric objects (e.g., the boundaries 508, 507, or 509 as shown inFIGS. 5A-B). In some implementations, the calculated SRV quantitiesassociated with each boundary, the calculated SRV uncertainty, thepercentage of the uncertainty over the SRV quantity, or a combination ofthese and other types of information can be displayed. In someinstances, one or more of the boundaries, the SRV quantity associatedwith each boundary, the SRV uncertainty, or other appropriateinformation can be displayed in real time during a stimulationtreatment.

FIG. 12 is a flow chart showing an example process 1200 for identifyingoverlapping stimulated reservoir volumes. All or part of the exampleprocess 1200 may be computer-implemented, for example, using thefeatures and attributes of the example computing subsystem 110 shown inFIG. 1B or other computing systems. The process 1200, individualoperations of the process 1200, or groups of operations may be iteratedor performed simultaneously to achieve a desired result. In some cases,the process 1200 may include the same, additional, fewer, or differentoperations performed in the same or a different order.

At 1202, a first subset of microseismic events can be identified. Thefirst subset of microseismic events can be associated with a first stageof a multi-stage injection treatment of a subterranean region. In someimplementations, the first subset of microseismic events can be selectedfrom a superset of microseismic events based on their respective timesbeing within a first time range associated with the first stage. Thefirst subset can be, for example, one of the subsets 610, 620, 630 and640 of microseismic events associated with a first, second, third andfourth stage of the multi-stage injection treatment in FIG. 6,respectively. The first subset may be selected from the superset basedon any additional or different criteria (e.g., location, event density,magnitude, moment, energy, or another suitable property).

At 1204, a first boundary can be calculated based on locations ofmicroseismic events in the first subset. In some implementations, thefirst boundary can be calculated according to one or more operations inthe example process 1000 or another technique. The first boundary can bea geometrical representation of the SRV for a first stage of amulti-stage injection treatment. For instance, the first boundary can bea corresponding boundary 710, 720, 730, or 740 in FIG. 7 given the firstsubset of microseismic events selected at 1202. The SRV for the firststage injection treatment can be identified based on the first boundary.

At 1212, a second subset of microseismic events can be identified. Thesecond subset of microseismic events can be associated with a secondstage of the multi-stage injection treatment. In some implementations,the second subset can be selected from the superset based on theirrespective times being within a second time range associated with thesecond stage. The second subset can be, for example, another of thesubsets 610, 620, 630 or 640 of microseismic events in FIG. 6. Thesecond subset may be selected from the superset based on any additionalor different criterion (e.g., location, event density, magnitude,energy, or any suitable property).

At 1214, a second boundary can be calculated based on locations ofmicroseismic events in the second subset. In some implementations, thesecond boundary can be calculated according to one or more operations inthe example process 1000, or another technique. The second boundary canbe a geometrical representation of SRV for a second stage of amulti-stage injection treatment. For instance, the second boundary canbe a corresponding boundary 710, 720, 730, or 740 in FIG. 7 given thesecond subset selected at 1212. The SRV for the second stage injectiontreatment can be identified based on the second boundary. In someinstances, the first and second boundaries are calculated in a commonspatial domain. The common spatial domain can be a two-dimensional spaceor a three-dimensional space. In some implementations, the second subsetof microseismic events and the second boundary can be associated with astage that is performed before, during, or after the stage associatedwith the first boundary. For example, when events belonging to anearlier performed stage do not support well for an SRV boundary or SRVfor this stage, the example process 1200 can start with a laterperformed stage and compute an SRV boundary for the later stage. The SRVboundary or the SRV for the earlier stage can be determined after thedetermination of the SRV of the later stage.

At 1220, based on the first and second boundaries, an overlap betweenSRVs associated with the first and second stages can be determined. Insome implementations, such a determination can include determiningwhether the first and second boundaries intersect. In someimplementations, identifying the overlap between the two boundaries caninvolve proper intersection, union, or other operations of the twoboundaries. In some instances, the overlap between the two boundariescan be identified based on the example procedure described with respectto FIGS. 6 and 7. For example, the first and second subsets ofmicroseismic events can be scanned to identify microseismic events thatlie inside both of the first and second boundaries. In someimplementations, intersected points that are intersected by one facet ofa first boundary and one edge of the second boundary can be identified.Similarly, intersected points that are intersected by one facet of thesecond boundary and one edge of the first boundary can be identified aswell. Based on the identified microseismic events inside both boundariesand the identified intersected points, a third boundary can beconstructed to represent the overlap between the first and secondboundaries. The volume of the third boundary can be calculated, forexample, as the overlapping volume of the SRVs between the first andsecond stages. In some implementations, additional or differenttechniques can be used for determining the overlap between the SRVsassociated with the first and second stages.

In some instances, a percentage of the overlapping SRV volume over therespective SRV quantities of the first or second stage can becalculated. The percentage of overlapping volumes over the SRV canquantify the treatment stage's efficiency of hydraulic fracture efforts.In some implementations, uncertainty of the overlapping SRV may becalculated, for example, according to the example process 1100 oranother technique. Additional or different metrics can be calculated,for example, to reflect communication of hydraulic fractures betweenmultiple stages.

At 1230, a total SRV can be calculated based on the SRVs associated withthe first and second stages and the overlap. In some implementations,the total SRV of a multi-stage injection treatment can be calculated bysumming up individual SRVs of each single stage and subtracting the SRVoverlap between adjacent stages. As an example, the total SRV for atwo-stage treatment can be calculated according to equation (6). In someimplementations, the total SRV may be calculated according to avariation of equation (6) (for example, including a scaling factor, aweight, or another parameter), or in a different manner. In someinstances, a percentage of the overlapping SRV volume over the total SRVof the multi-stage stage injection treatment can be calculated. In someimplementations, the percentage of each stage's SRV over the total SRVcan be calculated, which can characterize the contribution of thetreatment effects of the current stage's hydraulic fracturingstimulation to the hydrocarbons productivity of the overall treatmentwell. In some implementations, uncertainty of the total SRV can becalculated. Additional or different metrics can be calculated toreflect, for example, efficiency of the multi-stage injection treatment.

At 1240, one or more of the first, second, or third boundaries can bedisplayed. In some implementations, the boundaries can be displayedaccording to the example process at 950 in FIG. 9. For instance, one ormore of the boundaries can be displayed as geometric objects (e.g., theboundaries 710, 715, 720, 725, 730, 735, or 740 as shown in FIG. 7). Insome implementations, the calculated SRV values associated with eachboundary, the overlapping volume of SRVs between two boundaries, thetotal SRV value for the entire injection treatment, a percentage of theoverlapping SRV volume, uncertainty of the overlapping SRV or total SRV,or a combination of these and other types of information can bedisplayed. In some instances, one or more of the boundaries, the SRVvalues, or other information can be displayed in real time during astimulation treatment.

Although the example process 1200 involves a two-stage injectiontreatment, the example process 1200 can be adapted to more than twoinjection treatments or two stages of injection treatment. For example,a stimulation treatment or a stage of injection treatment may intersectwith more than one other injection treatment or stage of injectiontreatment. Overlaps among the SRVs associated with more than twoinjection treatments can be identified. A total SRV of the multipleinjection treatments or a multi-stage injection treatment can becalculated based on the SRVs for each stage and the overlaps, forexample, according to equation (7) or in another manner.

FIG. 13 is a flow chart showing an example process 1300 for real-timeSRV calculation. All or part of the example process 1300 may becomputer-implemented, for example, using the features and attributes ofthe example computing subsystem 110 shown in FIG. 1B or other computingsystems. The process 1300, individual operations of the process 1300, orgroups of operations may be iterated or performed simultaneously toachieve a desired result. In some cases, the process 1300 may includethe same, additional, fewer, or different operations performed in thesame or a different order.

At 1310, data for a new microseismic event is received. In someinstances, the new microseismic event is received in real time during astimulation treatment. The new microseismic event data can be stored ina buffer or other type of memory for further processing. In someimplementations, the location of the new microseismic event can bedetermined and its distances to one or more perforation clusters of theinjection treatment can be calculated and compared. A perforationcluster may include one or more perforations. In some implementations,the new microseismic event can be associated with the perforationcluster that has the minimum distance and the event can become asupporting event of the perforation cluster. In some instances, theexample process 1300 may not proceed to 1320 until enough data for newmicroseismic events have been received. For instance, a minimum numberof events (e.g., supporting events of a perforation) may need to beaccumulated before executing example operation at 1320.

At 1320, an initial boundary can be computed based on the microseismicevents. In some instances, the initial boundary can be associated with aperforation cluster. The initial boundary can be calculated based on thesupporting events of the perforation cluster. As an example, the initialboundary can be a tetrahedron constructed based on four supportingevents of a perforation cluster. The initial boundary can be of anothershape, and it can be calculated based on another number of events, forexample, according to one or more operations of the example process1000. In some implementations, an injection treatment or a stage of aninjection treatment may contain more than one perforation clusters. Inthis case, more than one initial boundary can be calculated based onrespective supporting events of the multiple perforation clusters. Insome instances, the perforation cluster can be regarded as the center ofthe calculated initial boundary.

At 1330, data for a new microseismic event is received. The newmicroseismic event data can be received in real time during thestimulation treatment. In some implementations, the new microseismicevent can be received after one or more boundaries (e.g., initialboundaries) have been computed. The one or more boundaries can bepreviously computed to enclose locations of prior microseismic eventsassociated with the stimulation treatment.

At 1340, a boundary is modified based on the data for the newmicroseismic event. In some implementations, modifying the boundaryincludes merging two or more boundaries into a single boundary, forexample, based on the location of the new microseismic event relative tothe centers of the two or more boundaries. As an example, two boundariesmay be merged together if a difference between the distances from thenew event to the centers of the two boundaries is less than a thresholddistance. Two or more boundaries may be merged based on other criteria.In some instances, the initial boundaries associated with respectiveperforation clusters can be merged into a single boundary representing astimulated volume for the received microseismic events. In someinstances, if the new microseismic event resides inside a boundary, theboundary may not need to be modified. If the new microseismic eventresides outside a boundary, the boundary can be identified and modifiedto enclose the new microseismic event, for example, based on a facetexpansion operation or other techniques. An SRV can be identified andupdated based on the calculated boundary in real time.

In some instances, modifying the boundary can include updating aselected subset of the microseismic events based on the data for the newmicroseismic event, and calculating the boundary based on the updatedsubset. In some instances, the selected subset of microseismic eventscan be updated by identifying and removing outliers and microseismicevents with low event density. Outliers and low density events can beremoved, for example, during a stimulation treatment, after acquiring ofmicroseismic event data, or from time to time. The outliers andmicroseismic events can be identified, for example, based on therespective statistical properties, tagged probabilities, or anotherattribute.

In some implementations, an uncertainty level (e.g., a probability) maybe associated with a new microseismic event. Based on the uncertainty ofthe microseismic event, uncertainty of the identified SRV quantity maybe calculated and updated in real time. In some aspects, the uncertaintyof the SRV may be used to monitor the accuracy of the real-time SRVcalculation as microseismic events accumulate in time.

In some instances, operations at 1330 and 1340 can be repeated until nomore new microseismic events are received, until a predetermined time,or until another terminating condition. The boundary can keep expandingas new microseismic event data gradually accumulate. In someimplementations, as more microseismic event data accumulate in time, theSRV estimation based on the updated boundary can become more accurate.In some instances, the real-time SRV calculation algorithm can producean SRV estimation with monotonically increasing accuracy.

At 1350, a post-acquisition boundary is calculated. The post-acquisitionboundary can be a boundary computed after the microseismic dataacquisition. In some implementations, a filtering operation (e.g., thefiltering operation at 930 in FIG. 9) can be applied to some or all ofthe acquired microseismic event data. The post-acquisition boundary canbe calculated based on remaining microseismic events after filteringout, for example, deterministic outliers, statistical outliers, lowdensity events, or other microseismic events.

At 1360, an SRV is calculated based on the post-acquisition boundary. Insome instances, the volume enclosed by the post-acquisition boundary iscalculated as the SRV for the associated injection treatment. The SRVcan be calculated based on the example process described with respect toFIG. 5A or in another manner. In some implementations, post-acquisitionuncertainty of the SRV or other information can be calculated.

In some implementations, the received new microseismic events and thecalculated boundary can be displayed in real time during the stimulationtreatment. For example, each time data for a new microseismic event isreceived, it can be displayed as a geometrical object (e.g., a dot) in aspatial domain, for example, as shown in FIG. 2A or 5A. A boundary, itscorresponding SRV quantity, uncertainty of the SRV, or other data can becalculated, updated, and displayed accordingly based on receivedmicroseismic event data. In some cases, the dynamic propagation andgrowth of the boundary can be displayed in real time. Users (e.g., fieldengineers, operational engineers and analysts, and others) can visualizethe geometry of SRV and identify the temporal and spatial evolution ofSRV in a real time fashion. In some implementations, based on theobservation of SRV evolution, injection treatment can be managed andadjusted accordingly to control the SRV development to maximize the SRVand formation production.

FIG. 14 is a flow chart showing an example process 1400 for identifyinggeometric properties of SRV for a stimulated subterranean region. All orpart of the example process 1400 may be computer-implemented, forexample, using the features and attributes of the example computingsubsystem 110 shown in FIG. 1B or other computing systems. The process1400, individual operations of the process 1400, or groups of operationsmay be iterated or performed simultaneously to achieve a desired result.In some cases, the process 1400 may include the same, additional, fewer,or different operations performed in the same or a different order.

At 1410, an SRV boundary is approximated or otherwise computed based onmicroseismic event data. The SRV boundary can be used to capture thegeophysical shape of a stimulated subterranean region and tocharacterize the geometric properties of the SRV for the stimulatedsubterranean region. In some instances, the SRV boundary can act as acontainer of identified microseismic events and stimulated hydraulicfractures (e.g., hydraulic fractures identified by fracture matchingtechniques). In some instances, the SRV boundary can be a boundary andinterface between the stimulated fracture network and the un-fracturedsubterranean region. The SRV boundary can include, for example, anellipsoid, a sphere, a cube, a cylinder, a polyhedron, a combination ofthem, etc. The SRV boundary can be symmetric, asymmetric, convex,concave, open, closed, or a combination of these and other properties.The ellipsoid 1509 in FIGS. 15B and 16A-B is an example SRV boundary.

In some implementations, the SRV boundary can be calculated based on theexample techniques described with respect to FIGS. 15-17, one or moreoperations of the example process 1000, or in another manner. In someimplementations, the SRV boundary can be computed such that it can fit aset of microseismic event locations. In some implementations, the set ofmicroseismic locations can be selected from the microseismic eventscollected for a stimulation treatment. The set of microseismic eventlocations can include, for example, the vertices of a computed SRVboundary (e.g., the convex hull 1508 in FIG. 15), locations ofmicroseismic events that reside around (e.g., within a thresholddistance to) a computed SRV boundary, locations of microseismic eventsthat reside beyond or about a threshold distance away from a referencepoint (e.g., the center of the collected microseismic events, thewellbore, the perforation clusters), or other locations. The SRVboundary can be computed based on post or real-time microseismic data,or a combination of both. The SRV boundary can be computed in real timeduring the stimulation treatment.

Taking an ellipsoidal SRV boundary as an example, an ellipsoid can becomputed, for example, to fit the vertices of a computed convex hull. Insome implementations, the ellipsoid can be represented by a generalellipsoid equation (12) with parameters a₁˜a₉. The parameters can benumerically solved using, for example, a least square approach (e.g.,based on equation (15)) so that the vertices have the minimum distancesto the ellipsoid. Numerical methods of Gaussian elimination or GaussJordan elimination, or another technique can be used to solve the linearsystem (15) to solve for the parameters a₁˜a₉ and in turn obtain theellipsoid. Additional or different techniques can be used to compute anellipsoid based on the microseismic event locations. As mentioned above,in addition to ellipsoids, other shapes of geometrical objects (e.g., asphere, a cube, a polyhedron, a cylinder, etc.) can be computed forcharacterizing the geometric properties of the SRV for the stimulatedregion. The other shapes can be computed, for example, in a similar ordifferent manner from the process described with respect to theellipsoid.

At 1420, a major axis of the SRV is identified based on the boundary. Insome instances, the major axis of the SRV can represent the lateralextension and orientation of the SRV for the stimulated region. In someinstances, the major axis can reflect the lateral extension andorientation direction of the primary fracture in the stimulated region.In some implementations, based on the computed boundary that capturesthe geophysical shape of the SRV, a major axis of the boundary can beidentified as the major axis of the SRV. For example, if the computedboundary is a cylinder (e.g., a circular cylinder, an elliptic cylinder,etc.), the axis along the height of the cylinder can be identified asthe major axis of the SRV. If the computed boundary is an ellipsoid, atleast one of the three semi-axes of the ellipsoid can be the major axis.For example, the three semi-axes can reflect the length, width, andheight of the SRV and the axis along the length of the SRV can beidentified as the major axis of the SRV. The major axis of another typeof boundary can be identified.

In the exemplary case of an ellipsoidal boundary, identifying the majoraxis of an ellipsoid can include, for example, transforming the generalellipsoid equation (12) into another standard ellipsoid representation,e.g., equation (16) with another nine parameters as shown in formula(19). As an example implementation, the transformation can involvecalculation of eigenvalues and eigenvectors of matrices. The “power”computational approach or another technique can be used for findingeigenvalues and eigenvectors of matrices. Among the nine parameterslisted in formula (19), four parameters can be identified and given moreweight in describing the geometric properties of the ellipsoid: lengthsof semi-axes (a, b, c) that can describe the length, width and height ofthe SRV and the rotation angle along the x-axis that can represent theorientation's azimuth of the SRV. These parameters can be calculated,for example, according to equations (27) and (30). In someimplementations, the larger value between 2a and 2b can be identified asthe length of the ellipsoid. The major axis of the ellipsoid can includethe semi-axis that corresponds to the length of the ellipsoid.Additional or different techniques can be used to identify the majoraxis of the ellipsoid. In some implementations, beside the major axis,other parameters or properties of the SRV boundary can be identified,for example, during the example operations 1410 and 1420. For instance,besides the four described above, the other five parameters out of thenine parameters in formula (19) (e.g., the center and the rotationangles around the y-axis and z-axis of the ellipsoid) can be identified,for example, according to equations (21) and (25). These parameters canbe interpreted and used, for example, at 1430 for analyzing thesubterranean region.

At 1430, the subterranean region is analyzed based on the boundary. Insome implementations, analyzing the subterranean region can includeanalyzing the volume and other geometric properties of the SRV for thestimulated region. For example, the volume of the boundary (e.g., theellipsoid) can be calculated as the SRV for the stimulated region. Insome implementations, the volume of the boundary can be calculated basedon one or more of the identified major axis and other parameters (e.g.,the length, width, height, radius, orientation, etc.) of the boundaryaccording to certain volume computation techniques, the example process1030 in FIG. 10, or in another manner. In some instances, the volume canbe easier to calculate based on the identified geometric properties ofthe SRV.

In some implementations, analyzing the subterranean region can includeidentifying or otherwise analyzing one or more of a length, a width, aheight, or an orientation of the SRV for the stimulation treatment ofthe subterranean region, for example, based on the geometry parametersor properties of the boundary. For instance, the length, width, andheight of the computed boundary can be used to approximate the length,width, and height of the stimulated region, respectively. In someinstances, the length of the stimulated region can represent theextension of the hydraulic fracture network to the reservoir while thewidth can relate to the number and the spacing of fractures in theprimary fracture family. In some instances, the orientation of the majoraxis of SRV can represent the orientation of the primary fracture familyin the subterranean region. For example, analyzing the subterraneanregion can include identifying or otherwise analyzing the fractureorientation associated with the stimulation treatment of thesubterranean region based on the major axis. In some implementations,analyzing the fracture orientation can include comparing the orientationof the SRV identified based on the major axis with the orientation ofthe hydraulic fractures identified based on, for example, fracturematching techniques. In some implementations, one of the two identifiedorientations can be used as a baseline to assess or confirm thecorrectness of the other.

In some implementations, analyzing the subterranean region includesanalyzing whether the identified length, width, height, orientation, oranother property of the SRV meet a respective criterion that reflects adesired length, width, height, orientation, or another property for thestimulation treatment. In some implementations, hydrocarbon productivityof the stimulated region can be predicted, calculated, or otherwiseanalyzed and the stimulation treatment can be adjusted or otherwisecontrolled, for example, based on the analyses of the subterraneanregion.

In some implementations, an uncertainty of the identified boundary, theidentified volume, major axis, or any other geometric properties of theSRV for the stimulated region can be identified, for example, based onthe uncertainty (e.g., in location, moment, time, etc.) of themicroseismic events. In some implementations, the uncertainties can beidentified according to one or more example operations of the process1100, based on probabilities, or in another manner.

In some implementations, the stimulation treatment can include amulti-stage injection treatment, and the example process 1400 caninclude computing a respective boundary for each stage of themulti-stage injection treatment (e.g., the ellipsoids 1715, 1725, 1735,and 1745 in FIG. 17) and identifying a major axis for a respective SRVfor each stage based on the respective boundary. In someimplementations, overlapping volume of SRVs between two boundaries, thetotal SRV value for the entire injection treatment, a percentage of theoverlapping SRV volume, uncertainty of the overlapping SRV or total SRV,or a combination of these and other types of information can becalculated, for example, according to the example processes 1200, 1300,or in another manner.

At 1440, the boundary is displayed. In some implementations, theboundary can be displayed according to the example process 950 in FIG.9. In some implementations, the boundary can be a container of themicroseismic events and identified hydraulic fractures. In someimplementations, the boundary, the microseismic events, and thehydraulic fractures can be displayed in the same domain, for example, asthe visualization 1600 a or 1600 b shown in FIGS. 16A-B. The boundary,the microseismic events, and identified hydraulic fractures can bedisplayed in another manner. In some implementations, the view of theboundary, microseismic events, and identified hydraulic fractures can beselected, rotated, enlarged, adjusted, or otherwise controlled by theuser, for example, as described with respect to FIGS. 16A-B. Forexample, a user may be allowed to open any facet of the SRV boundary toobserve microseismic events and identified hydraulic fractures inside ofthe SRV boundary. In some instances, the stimulation treatment caninclude a multi-stage injection treatment and the identified SRVboundaries and microseismic events can be displayed, for example, asshown in FIG. 17 or in another manner. In some implementations, thevolumes and other geometric properties (e.g., the major axis, length,width, height, etc.) of each SRV boundary, the overlapping volume ofSRVs between two boundaries, uncertainty of the volume or any othergeometric properties of the SRV for the stimulated region, or acombination of these and other types of information can be displayed. Insome instances, one or more of the boundaries, the microseismic events,the identified hydraulic fractures, or other information can bedisplayed in real time during a stimulation treatment. For instance, thedevelopments of the microseismic events, the hydraulic fractures, andthe SRV can be displayed. The visualization can provide detailed andquantified information of the SRV and help the field engineers and welloperators extract more accurate information (e.g., the lateral extensionand development of SRV at each stage) about the subterranean region andthe stimulation treatment.

In some implementations, some or all of the operations in the exampleprocesses (e.g., processes 900, 1000, 1100, 1200, 1300, or 1400) areexecuted in real time during a fracture treatment. An operation can beperformed in real time, for example, by performing the operation inresponse to receiving data (e.g., from a sensor or monitoring system)without substantial delay. An operation can be performed in real time,for example, by performing the operation while monitoring for additionalmicroseismic data from the stimulation treatment. Some real-timeoperations can receive an input and produce an output during a fracturetreatment; in some instances, the output is made available to a userwithin a time frame that allows the user to respond to the output, forexample, by modifying the fracture treatment.

In some cases, some or all of the operations in the example processes(e.g., processes 900, 1000, 1100, 1200, 1300, or 1400) are executeddynamically during a fracture treatment. An operation can be executeddynamically, for example, by iteratively or repeatedly performing theoperation based on additional inputs, for example, as the inputs aremade available. In some instances, dynamic operations are performed inresponse to receiving data for a new microseismic event (or in responseto receiving data for a certain number of new microseismic events,etc.).

Some implementations of subject matter and operations described in thisspecification can be implemented in digital electronic circuitry, or incomputer software, firmware, or hardware, including the structuresdisclosed in this specification and their structural equivalents, or incombinations of one or more of them. Some implementations of subjectmatter described in this specification can be implemented as one or morecomputer programs, i.e., one or more modules of computer programinstructions, encoded on computer storage mediums for execution by, orto control the operation of, data processing apparatus. A computerstorage medium can be, or can be included in, a computer-readablestorage device, a computer-readable storage substrate, a random orserial access memory array or device, or a combination of one or more ofthem. Moreover, while a computer storage medium is not a propagatedsignal, a computer storage medium can be a source or destination ofcomputer program instructions encoded in an artificially generatedpropagated signal. The computer storage medium can also be, or beincluded in, one or more separate physical components or media (e.g.,multiple CDs, disks, or other storage devices).

The term “data processing apparatus” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, a system on a chip, or multipleones, or combinations, of the foregoing. The apparatus can includespecial purpose logic circuitry, e.g., an FPGA (field programmable gatearray) or an ASIC (application specific integrated circuit). Theapparatus can also include, in addition to hardware, code that createsan execution environment for the computer program in question, e.g.,code that constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, a cross-platform runtimeenvironment, a virtual machine, or a combination of one or more of them.The apparatus and execution environment can realize various differentcomputing model infrastructures, such as web services, distributedcomputing and grid computing infrastructures.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, as well asdeclarative or procedural languages. A computer program may, but neednot, correspond to a file in a file system. A program can be stored in aportion of a file that holds other programs or data (e.g., one or morescripts stored in a markup language document), in a single filededicated to the program in question, or in multiple coordinated files(e.g., files that store one or more modules, sub programs, or portionsof code). A computer program can be deployed to be executed on onecomputer or on multiple computers that are located at one site ordistributed across multiple sites and are interconnected by acommunication network.

Some of the processes and logic flows described in this specificationcan be performed by one or more programmable processors executing one ormore computer programs to perform actions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andprocessors of any kind of digital computer. Generally, a processor willreceive instructions and data from a read only memory or a random accessmemory or both. A computer includes a processor for performing actionsin accordance with instructions and one or more memory devices forstoring instructions and data. A computer may also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto optical disks, or optical disks. However, a computer need nothave such devices. Devices suitable for storing computer programinstructions and data include all forms of non-volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices (e.g., EPROM, EEPROM, flash memory devices, and others),magnetic disks (e.g., internal hard disks, removable disks, and others),magneto optical disks, and CD ROM and DVD-ROM disks. The processor andthe memory can be supplemented by, or incorporated in, special purposelogic circuitry.

To provide for interaction with a user, operations can be implemented ona computer having a display device (e.g., a monitor, or another type ofdisplay device) for displaying information to the user and a keyboardand a pointing device (e.g., a mouse, a trackball, a tablet, a touchsensitive screen, or another type of pointing device) by which the usercan provide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well; for example, feedbackprovided to the user can be any form of sensory feedback, e.g., visualfeedback, auditory feedback, or tactile feedback; and input from theuser can be received in any form, including acoustic, speech, or tactileinput. In addition, a computer can interact with a user by sendingdocuments to and receiving documents from a device that is used by theuser; for example, by sending web pages to a web browser on a user'sclient device in response to requests received from the web browser.

A client and server are generally remote from each other and typicallyinteract through a communication network. Examples of communicationnetworks include a local area network (“LAN”) and a wide area network(“WAN”), an inter-network (e.g., the Internet), a network comprising asatellite link, and peer-to-peer networks (e.g., ad hoc peer-to-peernetworks). The relationship of client and server arises by virtue ofcomputer programs running on the respective computers and having aclient-server relationship to each other.

While this specification contains many details, these should not beconstrued as limitations on the scope of what may be claimed, but ratheras descriptions of features specific to particular examples. Certainfeatures that are described in this specification in the context ofseparate implementations can also be combined. Conversely, variousfeatures that are described in the context of a single implementationcan also be implemented in multiple implementations separately or in anysuitable subcombination.

A number of examples have been described. Nevertheless, it will beunderstood that various modifications can be made. Accordingly, otherimplementations are within the scope of the following claims.

The invention claimed is:
 1. A method comprising: collecting, by amicroseismic event sensor, microseismic event data representinglocations of microseismic events associated with a stimulation treatmentof a subterranean region; computing, by operation of data processingapparatus, a boundary based on the locations of microseismic eventsassociated with the stimulation treatment of the subterranean region,the boundary comprising a three-dimensional (3D) convex hull computedbased on the locations of microseismic events; computing a stimulatedreservoir volume (SRV) for the stimulation treatment by computing avolume of the 3D convex hull; and identifying a major axis of the SRVfor the stimulation treatment based on the boundary.
 2. The method ofclaim 1, wherein computing the boundary comprises computing anellipsoid.
 3. The method of claim 2, comprising calculating a volume ofthe ellipsoid.
 4. The method of claim 2, comprising identifying one ormore of a center, a length of a semi-axis, or an orientation of theellipsoid.
 5. The method of claim 2, wherein the ellipsoid isrepresented in the form${\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}}} = 1$and the major axis is the semi-axis of the ellipsoid that corresponds tothe larger value between a and b.
 6. The method of claim 1, comprisinganalyzing the subterranean region based on the boundary.
 7. The methodof claim 6, wherein analyzing the subterranean region comprisesanalyzing one or more of a length, width, height, or orientation of theSRV for the stimulation treatment of the subterranean region.
 8. Themethod of claim 6, wherein analyzing the subterranean region comprisesanalyzing fracture orientation associated with the stimulation treatmentof the subterranean region based on the major axis.
 9. The method ofclaim 1, wherein the stimulation treatment includes a multi-stageinjection treatment, and the method comprises computing a respectiveboundary for each stage of the multi-stage injection treatment andidentifying a major axis for a respective SRV for each stage based onthe respective boundary.
 10. The method of claim 1, wherein identifyinga major axis comprises identifying the major axis of an ellipsoid.
 11. Anon-transitory computer-readable medium storing instructions that, whenexecuted by data processing apparatus, perform operations comprising:collecting, by a microseismic event sensor, microseismic event datarepresenting locations of microseismic events associated with astimulation treatment of a subterranean region; computing, by operationof the data processing apparatus, a boundary based on the locations ofmicroseismic events associated with the stimulation treatment of thesubterranean region, the boundary comprising a three-dimensional (3D)convex hull computed based on the locations of microseismic events;computing a stimulated reservoir volume (SRV) for the stimulationtreatment by computing a volume of the 3D convex hull; and identifying amajor axis of the SRV for the stimulation treatment based on theboundary.
 12. The computer-readable medium of claim 11, whereincomputing the boundary comprises computing an ellipsoid.
 13. Thecomputer-readable medium of claim 12, wherein the operations compriseidentifying one or more of a center, a length of a semi-axis, or anorientation of the ellipsoid.
 14. The computer-readable medium of claim11, wherein the operations comprise analyzing the subterranean regionbased on the boundary.
 15. The computer-readable medium of claim 14,wherein analyzing the subterranean region comprises analyzing one ormore of a length, a width, a height, or an orientation of the SRV forthe stimulation treatment of the subterranean region.
 16. A computingsystem comprising: memory operable to store microseismic event datacollected by a microseismic event sensor, microseismic event datarepresenting locations of microseismic events associated with astimulation treatment of a subterranean region; and data processingapparatus operable to: compute a boundary based on the locations ofmicroseismic events identified in the microseismic event data, theboundary comprising a three-dimensional (3D) convex hull computed basedon the locations of microseismic events; compute a stimulated reservoirvolume (SRV) for the stimulation treatment by computing a volume of the3D convex hull; and identify a major axis of the SRV for the stimulationtreatment based on the boundary.
 17. The computing system of claim 16,wherein computing the boundary comprises computing an ellipsoid.
 18. Thecomputing system of claim 16, the data processing apparatus beingoperable to analyze the subterranean region based on the boundary. 19.The computing system of claim 18, wherein analyzing the subterraneanregion comprises analyzing one or more of a length, a width, a height,or an orientation of the SRV for the stimulation treatment of thesubterranean region.
 20. The computing system of claim 16, comprising adisplay operable to display one or more of the boundary, themicroseismic events, or a fracture associated with the stimulationtreatment of the subterranean region.
 21. The computing system of claim16, comprising a communication interface operable to receivemicroseismic event data during a stimulation treatment.